Highly unlikely. That's an ANCIENT wireless adapter by industry standards. We're talking wireless B here (circa 2002), not even G. And G is now being slowly replaced by N. You could always check the Linksys website for new drivers. But one reason I suspect it won't help is that WPA2/WPA requires more intensive processing than WEP, and a lot of older equipment simply can't be retrofitted to support it.
WEP if pretty much worthless anyway. Anyone w/ an interest can easily crack it within minutes w/ readily available tools off the ‘net. In all honestly, it's time to retire that adapter, esp. given how many reasonably priced replacement wireless G adapters w/ WPA2/WPA are available.