PIII motherboards would only support AGP graphics cards as far as I know.
Read the topic...
Anyway yes PCI -> PCI-E adaptors work fine
I have a old xeon (P4) server running with an adaptor and a asus 5850 card @ 400mhash/s so overclocking and overvolting works just fine the only problem i had was that i needed to short 2 pins on the adaptor because the motherboard wouldn't register the card while also using a 1x extender but otherwise you should be fine