Should a fuse with the correct amps, but is physically too small, still power my stereo unit?
It sounds like you have another problem.  Probably the problem that caused the original fuse to blow.  Although electrically, the 3/4 inch fuse is fine (the 250 volt rating is higher than the original which is OK) since the current rating is the same as the original, the fact that it is loose in the holder is not OK.  This can cause arcing as contact is made and unmade which could lead to a fire. It also can cause problems with the amplifier as the AC power is continually going on and off.  I recommend replacing the fuse with the proper size and then seeing what happens.