In previous years, I've noticed my tomatoes have root-like buds towards the base of the stem, but haven't wanted to experiment in case I wreck them.
Anybody had any experience of this? Is it worth it?
The hairs on tomato stems will turn into roots, given the right conditions (this makes taking cuttings of tomatoes extremely easy). If you let them grow along the ground, they'll root in various places where the vine touches dirt and stays reasonably moist.
As long as your compost is well aged, and won't burn the plants, there shouldn't be anything wrong with piling it up near the bases of the tomatoes. If it's not well aged, the microbes may cause some rotting, though. I generally prefer to top dress in rings around my plants, rather than pushing it up next to the stems.