I have used onboard amps in a few of my previous box guitars and not had a problem so long as I used a magnetic pickup (piezo discs would feedback if the volume was cranked up so these never sounded much louder with the onboard amp than just playing acoustically).
I always avoided gluing the speaker to the soundboard and instead fixed them to the back of the box. I used to use a 3.5W amp module made by Kemo based on the LM386 that is used in the pocket sized Smokey Amp that gets the volume by overdriving the signal. Adding a preamp would give greater volume overall and also give more headroom for a clean sound before the overdrive sound kicked in.
The volume I obtained was okay for bedroom playing and gave a good electric guitar sound. Not sure if it would be good enough for busking with background noise though.
David, big Thanks for your experience sharing. I have thought placing speaker on top side of box a good option. Will have a go at it with standard pup. Thx again!