I have on several occasions brought along a 8000BTU window air conditioner unit and setup on a board in the tent bed area we use for our daily catch all area. My 2KW Honda EU2000i runs it just fine.
We have the A/C sitting on a board over the mattress and then have the back of it sticking to the outside with the window flaps wrapped around the unit. It drains to the ground doing this and works great...
My 2KW Honda generator will not run my 13,500 BTU air conditioner at all so when I am off-grid I can bring along the 8000BTU unit and it works just fine...
Roy Ken