"It is hot here. Could we switch on the air conditioner?"
Sounds a little weird to me with the single-character verb. A little superfluous, because it doesn't provide any real assistance to the sentence.
I could be wrong, but personally I think I'd only use the 把 structure if the object were disposed of with a verb phrase. In this case, perhaps something like 我們可以把空調弄開嗎, which I don't think is a great sentence, but feels a little more comfortable to me structure-wise.
I know Duo has a sentence or two with 把 and 了 where the verb itself is a single syllable, e.g. 我把灯关了, but in such a case, something like 关了 can be thought of as a verb phrase, it seems to me.