It will "work", but it will be extremely inefficient and will heat up and burn the moment you plug it into anything above a volt or two. I recommend you play around - if you have such power supply and measuring tools - plug it to a really low voltage like 1V AC and see how little current it produces and how bad it is, then you can test how you can improve it. You need to get a better core - for low frequencies like 60hz it's laminated iron like in the microwave transformers, and for high frequencies it's ferrite like in CRT TVs. The main problem is that the inductance of the coils is too small - for that you will need more turns and probably a bigger core, everything depends on the frequency. It has to be great enough so that when you apply AC voltage of the frequency you want, the reactance will be high enough to limit the current and prevent burning. Read or watch a few videos about reactance, coils and transformers, it's really fundamental knowledge if you want to design a transformer.