He'd be cutting it close, but nothing wrong in trying. A newer card with possibly better DVI compliance should be dirt-cheap at this point (e.g., a used 9600/SE or 6200--I don't mention X300 b/c it's the PCIe version of the 9600, and I'm guessing your friend is running AGP or simple PCI). A 6200 would be more interesting if he'll be coding for games, as it supports SM3. Either way, aim for a fanless cooling solution: one less noise source or point of failure to worry about.
Actually, I haven't seen a DVI compliance test of a 6200, so I don't know if it passes at the 162MHz you'll want for the 2405's native res.
This is the only GF6 test I've seen, and it's not exactly encouraging. But I don't know personally how these less-than-perfect test results translate into display problems, if at all. That said, your 7500 looks to be as good as quite a few of the NV cards tested, so I wouldn't bother upgrading to a 6200 unless gaming or game programming is a concern.
Even though he won't be gaming, as an engineer he might be interested in
this 2405 issue (mind the flames), apparently specific to its DVI conxn. In summary, the slight lag is hypothesized to be due to Feed Forward buffering a frame or two, so a higher refresh rate should minimize it.