Nope, in Solo you are still affecting the BGS, tagging and mapping systems that legit players can't reach, etc, etc.More than likely, yes. However, in Solo, no one is affected by the fact that you're cheating. "Banned to Solo" means you're playing with yourself (no, not THAT way, dirty mind) so you no longer affect the BGS either.
This is why "Ban to Solo" is a joke of a punishment. FDev really need to grow a pair and do a very public wave of permabans -- like all credible MMO vendors routinely do.