It can cause a spongy pedal. With worn (scored/ridged) discs the clamping force is concentrated on a very small area of the pad (until it wears level to the disc) surface and in these high pressure area the can pad deform. More likely to be air in the OPs case though since a caliper was replaced.
+1
Though the effect is not great when only replacing single axle sets. However Brakes can feel very strange for the first hundred miles or so if you replace pads "All round" while retaining old disks! I advise people who wish to do this to do one axle at a time, a week apart if they do not want to replace disks at the same time!
The imperfect contact between new pads and old disks also means that all the heat of braking is generated at these points rather than over the whole disk surface. heavy braking before pads have bedded in can cause local overheating of the disks and is a major cause of disk warping after pad replacement. That is why you need to brake little and often untill the pads have bedded in propery.