Had your 6 months allowed visit already expired by the time you sent the application for the H visa? If it had, yes, you may be hassled because of the overstay.
If however you had applied to extend your stay before your 6 months are up, then you haven't technically overstayed, I think they consider your status as legal, but pending decision.
If you leave the country however, and if they deny your
TN visa, you may be subject to a ban, depending on how long you have overstayed.