The Japanese Vita FAQ, which initially noted that the Vita will play all downloadable PSP games except for Archives releases, cemented that in an answer to the direct question of whether or not the device will support old downoaded games. According to the FAQ, Game Archives games will not be compatible with the device at launch. "Plans for future measures will be announced shortly," the (Google-translated) FAQ notes.
There's no reason to suspect that there's a technical issue with running old PlayStation, PC Engine, and PS2 games on the powerful Vita. It's more likely that Sony's figuring out how to square the existing PlayStation Store for consoles with the PlayStation Suite version of the store, which offers a different and smaller selection of PSOne games. That hasn't been a problem so far ... because there hasn't been a device that could theoretically use both stores yet.