Will cracked manifold automatically throw code

If there is a cracked exhaust manifold, will a the check engine light, or another light, automatically come up and throw code or does it have to get worse to a point before that happens? And what is the difference between short and long tube headers from someone like Doug Thorley?

Thanks

 

It may or may not throw a code depending on the leak size and it also has to see that there is a problem.

LT usually deletes the cats which will throw a code without a tune or some type of O2 sensor defouler.