The PD 4000
series, including the 4045, are combo units that contain a converter and main AC (Alternating Current) breaker system. Leads to confusion in posts.
So yes, you could run your AC (Alternating Current) to the breaker box portion to power your AC (Air Conditioner). Did I mention confusion in posts?
I, personally, would prefer to have a battery in the 12 volt
DC system when the converter is powered and running. I don't know how the converter portion is powered in the combo units or if you can switch them off while there is AC (Alternating Current) to the unit.
I'm not necessarily a fan of combo units. I know my Inteli-Power is disconnected when it is unplugged. The main reason I like separate units is that when one thing breaks, it only affects on thing, not two (or more).
Good luck. It's way to hot to be trying to work inside your trailer without air conditioning.