Let us say I am flying a twin-engine aircraft and I got a engine failure during cruise, without any control on rudder and use the ailerons only, can I still maintain the target track or heading? Will I got any sideslip?
What will happen is the airplane will yaw into the dead engine, with a certain amount of roll into the dead engine, depending on how strong the dihedral effect, the roll-yaw couple, is. A swept wing airplane will want to roll upside down and it will take lots of aileron just to keep it right side up.
A straight wing airplane with moderate dihedral effect will require some moderate amount of aileron to keep wings level, and with wings level you will find yourself in a flat skidding turn into the dead engine with some aileron applied in the opposite direction - as if you were flying with both engines and applied rudder with opposite aileron to get the same effect.
To stop the turn you will need to introduce side slip that offsets the lateral lift coming from the skidding fuselage, and this side slip needs to be induced by bank, so enough extra aileron will be needed to lower the wing into the live engine until the change in heading stops. You normally lower the wing into the live engine about 5 degrees even with rudder being used normally, but in this case it'll take a lot more.
You will now find yourself flying more or less straight, that is, not turning, but with the nose skewed toward the dead engine, and quite a lot of bank into the live engine, whatever it takes to stop the skidding turn. You will be all askew but more or less proceeding in a single direction and it will be more or less the same as if you just applied rudder with opposite aileron induced bank to stop the skidding turn caused by the rudder application.
Adverse yaw from the aileron application will aggravate the situation since the down aileron is on the dead engine side, so adverse yaw is helping the live engine. And obviously, more power aggravates the condition compared to less power and you might find that wide open throttle causes more skidding than can be offset with bank and you run out of aileron and are force to reduce power.
So it might take most of the aileron travel to maintain this configuration, and of course the drag is so high that if you are in a piston twin you may not be able to maintain altitude at any height, even if you have ample power, because you might be forced to reduce power to keep the thing from rolling over as you run out of aileron.
If you're in something like a Seminole at 5000 ft, you might be able to maintain level flight in that condition, maybe if down around blueline speed, but I wouldn't be surprised if the best that you can do is a shallow descent as you're forced to lower the nose to keep from stalling in that skewed profile.
If you're taking multi-engine training, there's only one thing to do; go try it and see what happens and report back here.
You can use ailerons in cruise, but it gets dangerous if airspeed decreases towards stall (aileron reversal and live engine will cause roll/yaw into the dead engine).
With ailerons there will be a slip towards the live engine, which helps counteract the yaw away from the slip. The configuration will very much resemble a forward slip, with the accompanying increase in drag.
As the plane is banked and side slipping, an increase in throttle and some nose up trim will also be required.
Depending on the aircraft model, additional rudder (more coordinated) may work better than ailerons alone.