Yes, the model 65 can shoot any .38 Special. +P or otherwise. Just be aware that carbon rings will build up in the cylinder chambers and need to be removed or cleaned out after every range session.
A good solvent and copper brush should be able to get those out of the chamber. Many of us do that for our .357 magnum revolvers.
If you do not want to have to do that and want a .38 Special +P rated revolver only the Taurus 82 ( [video=youtube;mS53qZ0TjwY]http://www.youtube.com/watch?v=mS53qZ0TjwY]Taurus Model 82 - YouTube[/url] ) or a Rossi 851 ( Rossi 851 - YouTube[/video] ) will fill the bill.