If you are able to get the CTSA TL1 award, it is a pre-doctoral NIH fellowship. It will be fantastic for you... It adds credibility to your application.
You don't know if you will be selected for the TL1. Apply, you might make a late excuse if selected, after all, it is a competitive NIH fellowship and paid as compared to your unpaid volunteering. People understand a withdrawal for such a reason.
Sure. They are only offering an unpaid volunteering opportunity. Tell them that you sent an application to a very competitive funded NIH fellowship and you have a possibility for being selected, but that you expect to return to their lab.