Does the F5-ADD-BIG-ASM module increase the SSL TPS on an LTM-3600?

It actually depends on your platform. If you are on a platform that doesn't have all of its hardware SSL capabilities licensed out of the box, then yes the ASM license upgrades you to max SSL. That is still going to be hardware capped for the platform.

Viprion and 11050-11000 are the only platforms this is the case for.