Hi pyrofreak,
don't now, where your friend lives. In JAR land, treatment with anti-coagulants makes you unfit to pilot an aircraft (JAR-FCL 3.150). With DVT, there is the potential risk of embolic events to the lung, which doesn't go well with being PIC.
I doubt, that it is different in other regions of the world.
After ending the treatment, the medical can be reassessed (JAR-FCL 3, appenix 1 (11)).