Transformer AC doubler question

[VintagePC]

Just something odd I was curious about and thought someone here would know for sure.

Can one make an AC voltage doubler using only a center tapped transformer? It seems logical that it would work if connected like an autotransformer with no secondary - e.g. 120V AC to center tap and one leg, then getting 240v AC from one leg to the remaining leg.

Are there any problems with this method? I've been searching online and have found very little, perhaps because I'm using the wrong keywords, or because there's a reason this isn't done?

Does that still follow the standard inverse power calculation for a transformer (2x voltage = 1/2x current) or is it different because there's no secondary in use and the full current going in comes out?

I realize there's probably a simple answer but I've been wondering about this for so long that I'm starting to overthink it. :/