We had a fleet of PCMCIA cards for wardriving in the early 2000s, but only one for 802.11a.
It was rare to find, but the networks were left weirdly open, presumably because it was rare, limited range, and they didn't care to troubleshoot security on top of connectivity.
Yeah, but certainly wasn't common until 802.11n 5GHz stuff shipped and became in common consumer use. The target market for a psp would have had 802.11b or .g 2.4 GHz only home routers/APs. Think Linksys wrt54g and similar.
It's exceedingly unlikely to find something from the time of the psp in 2003/2004 that has 802.11a 5GHz and isn't a business laptop.