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I wouldn't rent somewhere without a/c so if the going rate for units with that were higher compared to ones with no a/c, the I'd pay extra for that. And I would expect it to work and take the necessary steps if it didn't.
But no, I would not pay more for a unit with a newer a/c vs older - that's part of the landlord's cost of doing business, to keep it in good operating condition, and if necessary, to replace it.
Now, having said that, if the entire unit were updated - new flooring, nice stainless appliances and granite or quartz counters, and new systems like a new a/c, then presumably that would command a higher rent.