TX has said it would recognized nonresident permits for TX residents.
However, I would personally contact them if I were in that situation to have a communication to that effect.
Whether the police know this is another question - you might take the ride.
Texas makes no distinction between resident and non-resident permits. Texas DOES have a reciprocity agreement with Florida where each agrees to honor the other's permits and this has been in place 10 years.
So yeah, whether the police know it or not is sort of the risk everyone runs with all the laws. The police certainly don't know everything. However, I haven't heard of anyone getting busted for carrying a gun with a permit from another state that is honored by Texas. It has probably happened, but then again there were those who initially got hassled when Texas first introduced the CHL program and certain LEOs did not wish to honor the new law...just as a few threatened not to do with legalized concealed carry in automobiles. They all got appropriately squushed with time, however.