Viable to slip onto the center line?
Yes, we can use a sideslip to shift the aircraft sideways relative to the runway, without changing heading. More on this below. However, the body of the question contains some misconceptions--
I am wondering about the viability of side slipping onto the line
instead of doing banking maneuvers. In other words, there would be no
bank and no turn.
This excerpt shows a misunderstanding of basic flight dynamics. The fundamental characteristic of a sideslip is that the aircraft is moving sideways through the air. As an aircraft enters a sideslip, there's generally going to be a bank, a turn, or both.
If rudder is applied and held while the ailerons are manipulated as needed to keep the wings level, the aircraft will fly sideways through the air (sideslip), and the aerodynamic force resulting from the air striking the side of the fuselage will cause a curvature in the flight path-- a turn-- in the direction of the deflected rudder. So now we're actually in a skidding turn.1 The aircraft's heading will change. You could steer the aircraft closer to the runway centerline this way, but why would you? Much better to turn the normal way-- by banking. Skidding turns are generally considered to be bad airmanship, and an invitation to a spin.
On the other hand, when we talk of "sideslip" we often envision a maneuver where the aircraft is kept in a bank opposite the direction of the rudder input. For a typical "forward slip" to increase the descent angle and sink rate, we would apply rudder, moving the nose to a different heading and exposing the side of the fuselage to the airflow, while simultaneously applying bank as needed to provide a sideways force that cancels the aerodynamic sideforce from the sideways airflow striking the fuselage, preventing the flight path from curving in the direction of the applied rudder. So we're now flying sideways through the air, but the direction of the flight path and ground track hasn't changed-- this won't bring us any closer toward the runway centerline.
Alternatively, we could first apply the bank angle, while manipulating the rudder as needed to prevent any heading change at all. This is the typical "sideslip" that we do to compensate for a crosswind on final approach. Aerodynamically, for any given bank angle, this kind of "sideslip" ends up being exactly identical to the "forward slip" described immediately above-- we've just entered it slightly differently, giving the flight path and ground track some time to change direction (toward the low wing) before the full rudder correction is applied.2 So we've actually accomplished a turn as we entered the maneuver-- we've angled or "bent" the direction of the flight path and ground track toward the low wingtip.3 Once the maneuver is stabilized, with constant bank angle and rudder deflection and heading, the flight path and ground track are linear again, but no longer aligned with the aircraft centerline (at least in the no-crosswind case). The fuselage ends up moving sideways through the air, like in any other sideslip.
We could use this maneuver to move toward the runway centerline without changing heading. (Not to move toward the runway centerline without banking.) And for small corrections, this may be in fact what pilots sometimes (perhaps unconsciously) do, especially when very near the runway. Of course, the wings should be leveled again (in the no-crosswind case) to stop all sideways "drift" before touchdown-- touching the ground while moving in a different direction than the aircraft is actually pointing can be hard on the landing gear. For larger corrections, carried out higher from the ground, it's generally better just to do a shallow turn toward the centerline, "coordinated" in the usual manner.
For completeness, we should also note that in the case described immediately above, when we remove the bank and the rudder input to exit the sideslip, without allowing the aircraft to change heading, we again accomplish a "turn"-- we "bend" the direction of the flight path (and the ground track, in the no-wind case) so that they are again parallel to the direction the aircraft's nose is pointing. Technically, this could be described as a very slight "skidding" turn-- as we are taking out the bank angle, we delay taking out the rudder input for just long enough to allow the sideforce from the air striking the side of the fuselage to "bend" the flight path and ground track in the direction of the deflected rudder (i.e., toward the high wingtip.) You'll never see this maneuver analyzed in this level of detail in any flight training materials--and knowing this extra detail won't make your landings any better-- but that's in fact what is going on. From the pilot's viewpoint, however, it's simpler just to focus on the fact that by banking the wing, without allowing the heading to change, the aircraft is being "slid" sideways toward the low wingtip, and this "sliding" ends once the bank is removed.4
The language gets kind of complicated here. To an engineer, any sideways motion of the aircraft through the air is a form of a sideslip. To a pilot, if the sideways motion is toward the high wing, or if the wings are completely level, the maneuver is called a "skid" rather than a "slip" or "sideslip".
This, in a single sentence, is the slight difference between the control inputs used to enter the maneuvers commonly described as a "sideslip" and a "forward slip". Pertains to many other ASE questions -- such as this one: What is the difference between a forward slip and a side slip? . No suggestion is intended here that a pilot is typically aware that he or she is doing something slightly different with the rudder when entering a forward slip versus a sideslip-- it's just a natural result of the pilot's intention to either keep the aircraft's heading constant during the entry, or to cause it to change.
Of course, the "turn" we're talking about here is quite modest-- for the aircraft heading to stay constant, the direction of the flight path through the airmass must "bend" or change by an angle that is exactly equal to the angle between the direction of the flight path through the airmass and the direction the centerline of the aircraft is pointing. I.e., by an angle equal to the yaw string deflection, in the case of a "perfect" yaw string mounted on a long probe well in front of the nose of the aircraft.
This simplification-- focussing on the sideways "sliding" aspect of the maneuver while ignoring complete dynamics of the actual turns that take place as the maneuver is initiated or terminated-- arguably has tinges of an Aristotelian rather than Newtonian understanding of physics-- one can easily draw the incorrect conclusion that a steady net force is required to cause a steady linear motion.