I'd do a thorough job of cleaning any used tank - vinegar to break down calcium/lime, then bleach with thorough rinsing...
I'd replace the gravel and also do a thorough cleanup on the filter.
Bottled products in theory can help, but have received mixed reviews. Your best bet IMHO is to get some media (filter floss) or objects with surface area (a rock or other decorative item?) from an established tank (don't let it dry out/delay, treat it like a living thing in a bag with water, etc) and follow the fishless cycling as described in the FAQ.
If you're lucky? Some speak of 2 week cycles. I'd still plan for double that. It's tough to wait through the whole thing, but I'm guessing your fish will thank you.
Your last question - the answer is probably if the bacteria are still alive - but I'd think that the delay and adverse conditions of the purchase/ship process would kill the bacteria you want. And you might inherit diseases or parasites from the previous owner.
I'm personally skeptical of the promise of rapid cycling - but that's just based upon all the research I've done and cycling my own tank. Probably not what you wanted to hear, I know... I for one with there truly was an overnight or 1 week way to cycle a tank.