Those that were allowed to re-enlist, joined a variety of units. Some as far away as Kentucky. Some went into other Louisiana Units in Virginia. I would suspect that there was a bit of pride in being in Wheat's, so that is the unit they put down as their unit. My recollection is that the paperwork also inlcuded their current unit too. Being in Wheat's was such an honor, I have found soldiers saying they were in Wheat's, but no documentation as to them being so.
I would suspect that those soldiers that were not allowed to re-enlist went home to Louisiana or elsewhere. As the war ended, the US Government may have wanted an accounting of all soldiers of the confederacy, and to get their paperwork done (allegence, parole, etc). As they did not join another unit, they put down Wheat's as their unit.
Smarter people may be able to give a better reading than I as it relates to this.
JIM T