No. Having FVL should not interfere with your immune system. The only time you are at a higher risk of sepsis is when you have something that compromises your immune system.

The immune system and the coagulation system are linked

Interesting topic!! I am a research scientist with the NYSDOH, and I read in a Scientific American a few yrs ago that the opposite actually holds true- You are LESS LIKELY to develop sepsis when you have a clotting disorder. Finally, a positive attribute :)