Learning Fedora will certainly not hurt you at all. It will give you everything you need to know for the TIA Linux certification. You will know about 95% of what you need to get your RHCT.
I think the TIA Linux certification is mostly a multiple choice exam. I have not taken it so I do not know for sure.
The RHCT exam is pretty straight forward. It changes from time to time, but not too much. They will give you three tasks:
1. They will set you down in front of a PC that fails during boot up. You must fix it.
2. They will ask you to do a basic Red hat install (the options you are expected to use will be on a list).
3. They give you a list of users. You will have to set up accounts based on the list.
You can use the GUI, the command line functions, or you may edit the etc/passwd, and atc/group files using vi or vim. It makes no difference, oo long as the tasks are completed successfully.
You can buy a second hand copy of RHEL (still in the original sealed box) off e-bay, and buy all the books from half.com. You can also take classes at your nearest Redhat University. I did both.