Would the answer be different for a fixed wing glider that has all control surfaces locked in a neutral position? In other words, does the self-adjusting/ pendular pitch of the parafoil affect the IAS it stabilizes at?
You seem to have an intuition that a parafoil (or paraglider or hang glider) tends to trim to a constant pitch attitude, and that this is somehow different from a more conventional aircraft's tendency to trim to a constant angle-of-attack. In reality -- at least as long as we make no changes in the aircraft's configuration (physical shape), and we don't introduce Thrust into the picture, these are just two different ways of describing the same thing.
In an unpowered glider, the glide ratio with respect to the airmass is determined by the L/D ratio. We can think of the glider's pitch attitude as being the result of the angle-of-attack minus the glide angle relative to the airmass; this result may be either positive or negative. Also note that as long as we make no changes in the configuration (physical shape) of the aircraft, and as long as we don't introduce a thrust force from a motor, then each possible value of the L/D ratio, and thus each possible value of the glide angle relative to the airmass, corresponds to one particular angle-of-attack. Therefore, tending to trim to a constant pitch attitude is the same as tending to trim to a constant angle-of-attack--either way, the glider will trim to a given glide ratio, and a given Indicated airspeed. So the answer to your question is "no".
Now, if we were varying the glide ratio by deploying wing-mounted spoilers, or by adding some power, then in an aircraft that tended to trim to a given pitch attitude, that would generate a change in angle-of-attack, and therefore a large change in Indicated airspeed1, even if the spoilers (or the thrust line) generated no pitching moment relative to the aerodynamic center of the aircraft.
One way to understand this is to note that the aerodynamic center is far above the CG in an aircraft that relies on "pendulum stability", so a force that passes directly through the aerodynamic center of the aircraft, and therefore acts with zero moment-arm relative to the aerodynamic center of the aircraft, still generates a strong pitch torque relative to the CG of the aircraft.
If we introduce a thrust force that acts through the CG of the whole system, rather than the aerodynamic center of system, we'll find that the wing still tends to trim to a constant angle-of-attack (and thus a nearly constant airspeed2) as we vary the thrust force, even though the pitch attitude will vary with the climb or descent angle.
So even though the "pendulum stability" provided by the arrangement of the CG far below the aerodynamic center of the wing does play an important role in the flight dynamics of parafoils, paragliders, hang gliders (in the case where pilot is holding a fixed position in the control frame), etc, it's not really true that such aircraft have an absolute tendency to trim to a fixed pitch attitude. But for the simple case of steady-state3 wings-level gliding flight in a fixed configuration, that is a valid way to look at the dynamics.
Footnotes:
Consider an aircraft whose trim characteristics are such that it perfectly holds a given angle-of-attack regardless of changes in thrust, or changes in configuration that increase the drag coefficient (without affecting the lift coefficient). Even such an aircraft will still experience some change in Indicated airspeed when the Thrust is altered, or when the drag coefficient is altered. The reason for this is that the total Lift required for steady-speed (wings-level) flight is not constant, but rather varies according to the sine of the descent or climb angle. For more, see this related ASE answer: Does lift equal weight in a climb?
See footnote (1).
For further insight into what "pendulum stability" does and does not mean, search up some videos of hang glider and paraglider aerobatics. Though limited to positive G-loadings, the maneuvers that can be performed in such aircraft may surprise the reader!