It is an interesting topic, having spent a little time looking at typical switch mode circuits it seems to me that the answer is, sadly, it depends. (warning, not a professional just a keen amateur wrt electronics)
If your power supply is a traditional linear power supply (Transformer->bridge rectifier->smoothing cap) it certainly will not work at 400hz.
If you have a switch mode power supply it appears initially to be simple as the AC is first rectified to DC then smoothed so what difference does input freq make? The higher the frequency input the smaller the input smoothing cap needs to be so it should work well at 400hz. Indeed looking at the smaller switch mode circuits I can see no reason they will not work well.
My only concern would be a switch mode power supply with passive power factor correction (PFC mandated on SMPS above 75 watts in the EU, this is more powerful laptop than ipad/phone territory). The point of the filter is to pass line frequency and block harmonics of the input frequency. 400Hz I think would be filtered by the PFC, I can't imagine it would do the inductor much good trying to run a SMPS with passive PFC on 400hz.
Does anyone here know more about PFC / AC harmonics/ power factor etc and can give professional opinion?