Proper answer is "I don't know", but in a attempt not to be boring, I'll go with "I don't think so". My understanding of the underlying process is shaky at best but it seems to me the actual "infection" stage, where the virus does damage is mostly limited to two-three weeks. There are extreme's where it's much longer and for most it's shorter but for a ball park figure that seems about right.

The problem is given that the virus can effect (damage) blood vessels, it can effect every part of the body. I'm still iffy on the viability of replication outside some of the sweet spots like the lungs etc. Even though the window for actual damage from the virus would then be short the cascading effects can linger and present with delay.

That might be all wrong though, if it even makes sense.