Yes and no, you can run the max tire psi. But that is recommended for max tire load. It will help, but not as much as a higher load rating tire at a higher psi. If you get the soft, floating, not secure feeling I would up the psi.
Got more specs on what you are carrying for a load?
2006 2500HD Duramax CCSB 2WD
2014 Crusader 285RET
Nights camped in 2013 - not enough!
Nights camped in 2014 37
Nights camped in 2015 40
Nights camped in 2016 35