If you can play games at what you consider playable framerates, and visual details aren't too far from reviews from 2003/2004 - it should be fine.

Faster CPU is nice but make sure your board supports it before buying.

I remember that HP Compaq NX7010 laptops used Pentium 4 2.8GHz processors (Nothwood 533Mhz FSB). So if the laptop cooling somehow managed to do it, your desktop should be able to do it too.
The question is whether your headboard supports FSB 533 ?
As for Pentium 4-M support, it can be worse (for example, that NX7010 did not recognize such a processor). But you won't be convinced unless you try to do it...