I can tell you that I have taken media, and sponge filters from established tanks and "instantly cycled" tanks several times, and never had a problem. However in all these cases, I was adding what most would consider very small bioloads (usually a pair of dwarf cichlids in a 20g or 10g tank). The thing that takes so long with cycles is starting from scratch. A handful of bacteria colonizing your tank and then reproducing by splitting takes several weeks to reach numbers that can handle fish waste. The growth is logrithmic however and once you get a good colony of bacteria, they can repriduce very fast to meet new bioloads. In new cycles you also have to wait for this happen twice, once for the ammonia > nitrite bacterial species and again with the nitrate > nitrate species. (about 4-6 weeks). Your "pre-conditioned" media already has large numbers of both types of bacteria.
Since betas are often kept in bowls with no filtration at all, I would think it would certainly be ok to add it right off the bat. I think the snails would be fine too, but if you're worried wait a week on them. Lastly, it certainly wouldn't hurt to dose the tank with ammonia especially if you've already got it. It should only take 24 hours for the bacteria to metabolize it.