An individual can file for bankrupcty in Louisiana even if they're a general contractor, yes. However, that bankruptcy filing could potentially impact a contractor's license.
The bankruptcy code blocks a state from revoking a license because the licensee has gone bankrupt. However, the state licensing board will likely scrutinize the bankruptcy filings to check for misappropriation or mismanagement, plus it may be hard to prove financial stability to maintain that license going forward. To be sure, it appears that a contractor will need to immediately notify the board of the bankruptcy, as well.
Admittedly, I don't have experience in licensing or bankruptcy - so consulting a Louisiana bankruptcy or construction lawyer who's got experience in those areas would likely be a good idea. If you're navigating bankruptcy, or if you're reviewing it as an option, your bankruptcy attorney should be able to help with that.