You certainly don't have to go though CTY to take SAT. You can just register with college board. Then you can send the score to CTY or other programs. It may save you $40, I am not totally sure.
CTY offers full Talent Search benefits in 19 states and DC. It means that CTY holds awards ceremonies in these states for top scoring students. But anyone can apply CTY. Most of those who did that for summer program purpose.
Those summer programs are not cheap. Usually around $1000 per week so a 3 week residential camp sets you back $3000. There are some free summer camps like RSI but very difficult to get in. Some residential math programs are relatively inexpensive.
