Maybe, maybe not. And no, you will never see a "frequency" switch.
The first thing I would do is look at the nameplate and the instruction book. Computers are made for the world market and many will auto switch or have a voltage selector switch. If this is the case the different line frequencies will not matter either.
If you really want to be sure otherwise I would contact the manufacturer. Switching power supplies could have problems with different line frequencies unless they are designed for it.
Most PCs use switching power supplies. And most of those power supplies convert the incoming AC into DC, then convert that to high frequency AC to feed a small high frequency transformer, then on the secondary side of that transformer convert it to various DC voltages (12V, 5V and such). Such supplies don't care about powerline frequency as they convert to DC anyway (rectifier diodes and filter caps). Most have a voltage selector switch, this rectifier/cap circuit is a voltage doubler (in 125V mode) or a bridge rectifier (in 250V mode). You could run it off of a DC source of 300VDC if it's set for 250V. The bridge rectifier would just automatically correct the input power's polarity and feed it to the filter caps.
Only if the supply has a circuit that does something about the harmonic content of the current it draws off the powerline could the powerline frequency matter, and most likely it could accomidate 50 or 60Hz anyway. The harmonic currents that tend to overload neutrals in a room full of servers fed by 3 phase 120V power.