Technical reviews I looked at recommend a high quality 500 to 550 watt power supply with a 12 volt rail rated at 40 amps for an overclocked Intel Core i7 system with the pre-overclocked version of the GTX 260. That's a fairly common recommendation with a lot of the newer high end systems and viddeo cards. Your Corsair VX450 has a 12 volt rail rated at 32 amps which may or may not be okay.
In addition, that overclocked GTX 260 requires two 75 watt, 6 pin, PCI-e, power connections. The Corsair VX450 only comes with one. That's not a total disaster as a molex to 6 pin adapter could be used.
Finally, as you already know, you have an old system that does not require as much power during gaming as some of the new high end systems. Again, you "might" be okay but I'm inclined to say your system may not be able to keep up with the capabilities of the new, high end, overclocked GTX 260.
Some of the things that can happen with an underpowered system are bad 3D performance, crashing games, spontaneous reset, shutdown of the PC, and freezes during gameplay. PSU overload can cause it to break down.