Thank you so much for rescuing this cat.
At four months, he's still relatively young, and based on the simple fact that you were able to pick him up, I think there is an excellent chance your cat will be happy inside. If truly feral, he wouldn't have let you pick him up. Ritz and her litter mates were successfully socialized at around six months old, and some cats I re-trapped after TNRing (long story) were closer to one year; they have been adopted into Furever Homes.
Just give him lots of time to get to know you. Sit with him in the bathroom, reading aloud quietly and working on the computer, etc. Let him sniff your finger(s) if he approaches. Move VERY slowly at all times. With Ritz, I told her what I was going to do (still do): "I'm getting up now"; "I'm behind you", etc. This gets your kitty use to your voice. And enter with treats in hand; a way to a cat's heart is (initially) through his stomach
Regarding additional costs, the main one with be neutering. Check around your local non-profit SPCAs and rescue organizations. Where I live the cost is anywhere from $60 (non-profit) to $300 (vet). Many clinics as part of spaying/neutering, will also de-worm. (And, it's a given that the cat has worms. Comes with the territory of living outdoors.) They may also offer FIV/FeLK testing at a reduced cost.
And in answer to your question: yes, there are some cats who cannot adjust to an indoor lifestyle. Some cats simply don't have it in their "DNA". Some cats were too abused when a kitten to ever trust humans or lived on the streets too long. But your kitten sounds lovely, and a good candidate for a happy indoor cat.
PS: we looovveee pictures