Don't screw up the fuses. 
There are some clock settings that are very annoying for recovery but disable-reset is the critical one.
Is it just that most boards don't give access to the XTAL pins...
That would certainly make HVP difficult.
...or would the signal not work if a crystal or resonator were installed.
I assume a crystal/resonator and the capacitors would interfere. I have no idea if they would prevent HVP from working.
Most boards have a resistor and/or a diode between /RESET and VCC. That is going to interfere with any attempts to put 12V on /RESET.
Hence removing the chip (if possible) is probably the only option. I suppose you could cut the trace to /RESET but it might be difficult.
Actually, that is I suspect, the beauty of it - a crystal and capacitors (remember, the capacitors are 22 pF or similar and the crystal not a great deal more) should not interfere with programming, merely slow the transitions a little - having a HCMOS gate connected to a crystal terminal should easily override the crystal.