Two pre-amps in the signal path isn't a problem in itself - you already have two pre-amps between your source and subwoofer...care just needs to be taken setting up correctly.
The main thing to consider is exactly what you're looking to improve. Adding a high quality stereo amplifier will improve the quality you will get from your left and right speakers. This can be a massive improvement for music listening, though will only be a partial improvement for movie viewing, although if this is secondary or occasional to music, it won't be an issue. The left and right speakers usually deal with music, left/right effects, and back up the centre when there's a lot going on, so these aspects will be improved. Care is needed if the AV receiver is vastly different in quality to the stereo amplifier being used, as the centre will be using the AV receiver's pre-amp so it's quality isn't changing at all. The centre channel is probably outputting more sound than the rest of the speakers put together, so it is this channel that it the most important.
If you're into older movies that are only in stereo, or mono where the single channel has been shared by the front left and right (2.0), and you are the type of person who listens to these movies in their native audio, then these movies will greatly improved!
Adding dedicated power amps will improve power delivery and control - general quality won't be improved as you're still being held back by the pre-amp section.