If the board does not support the CPU, it likely won't POST, but if you have everything available on-hand it should only take a few minutes to find out whether or not it works. I'd also be a little concerned about it having a fit over the RAM likely having different timings (it *should* just default to whatever is common, which will likely mean DDR2-533, but it may not figure that out as smartly as you'd like). Depending on what the Celeron actually is, the cooling solution will probably work with the Core 2 as well.

PSU wise, it really doesn't need to be anything insane - X800 and Core 2 Duo really aren't that power hungry, but it will require most of its power via the 12V rail. A modern ~400W PSU should have no problems with this machine, but an ancient unit that can only drive 8-10A on the 12V wouldn't be a good idea.

With the E6300 running at stock speed 15A on the 12V rail should be enough to power the system.

That board dosnt have any AGP/PCI lock so do not overclock the CPU beyond 300 MHz FSB which gives you 2100 MHz or strange things will happen.
With the CPU overclocked you will need another ~2A on the 12V rail.

I don't really care if it's not going to work 😁
Thank you for the advice!

I hope it works!
I had a similar idea so I'm building a machine that has the best win98 official-compatible hardware.

That is:
Asrock 775i65g r3.0 motherboard from 2012 (!!! - i865G, core quad support) http://www.asrock.com/mb/Intel/775i65G%20R3.0/
Pentium Dual Core E6500K (unlocked multi, 1066FSB) (should be able to reach E6800 speeds easily)
2x1GB Dual Channel RAM (going to limit this at win98)
Gainward GeForce 6800 Ultra AGP 8x
(will se if I plug an SB Live! and a Voodoo²)

It's nice to have a system that can run Windows 8.1 (and Win 10 later this year) pretty decently yet supports Win98SE officially! 😉

I will get a 450W PCIe PSU for tests and give it a try as soon as I get new thermal paste 😀
(Arctic Cooling MX-4)
Thank you all for your advice!

That board won't support any Core 2 Duo processor. The best you can hope for is a Pentium D which is still better than nothing 😉

The manufacturer hasnt updated the CPU support page or many people on different forums are very confused.

A quick search shows many people claiming it works so I would at least try. Be sure to flash the latest BIOS.