No. If one testicle's removed, due to something like cancer, the other one's quite capable of working. It's unusual for cancer to effect both, but if both WERE to be removed for any reason, then sperm'd no longer be produced, and long before that, chemotherapy'd slow the production of it down anyway.
Interesring point by Ice Maiden.......it is very UNUSUAL to remove BOTH testicles for testicular cancer. Also the post surgery treatment may affect the spem production.
Presumably you are interested from a personal point of view in regarding having children, in which case a sperm count would be advisable.