Re: TBH and moving in a swarm?
Welcome to Beesource!
Yes, you could just shake the collected swarm into the TBH. However, the sooner that this happens after they are collected by the "swarm catcher", the better.
Absolutely, there is a chance they will not like your hive and abscond. I would recommend putting 3-4 drops of lemongrass oil (LGO) on the wood inside the hive. Do not overdo the LGO! If your TBH has an open screened bottom, close it off with a board at least until after the colony has built comb and brood.
Don't count on getting honey this year. The bee and weather gods may smile on you, or not!
Read Michael Bush's comments about TBHs and in particular, comb guides, here:
USDA Zone 7a - elevation 1400 ft