Post-JD banking and clerkships

I'm a 3L in law school, still undecided between biglaw and banking as a post-JD associate. I've considered applying for full-time positions right after graduation, but I have a federal clerkship which lasts for a year and starts around late July, and it's considered beyond the pale to back out of these, would seriously hurt legal recruiting if I did go into law, etc. 

Would it be feasible to try to get a summer internship at a bank between graduation and clerking, and then go to the bank after the clerkship?