You could profile it and find out.

Another commenter pointed out that compilers have very different performance characteristics to games, and I'll include web servers in that too.

tsc needs to start up fast and finish fast. There's not a ton of time to benefit from JIT.

Your server on the other hand will run for how long between deployments?

If your backend is JS and it's too slow for you, then obviously porting it to a machine code binary will speed it up significantly. If you are happy with your backend performance, then does it matter?