A GFCI extension cord adds protection.

Yes. The GFCI is built into the cord itself, so it doesn’t matter if the wall outlet is protected or not. Plugging a GFCI cord into a non-GFCI outdoor outlet works exactly like plugging a GFCI cord into a GFCI outlet: it will trip if there’s a ground fault downstream (i.e., in whatever you’ve plugged into the cord).

The only catch is that the GFCI cord only protects what’s plugged into it, not anything else on that circuit. So if you’ve got multiple outdoor outlets sharing the same breaker, only the one with the GFCI cord gets the protection. That’s still way better than nothing.

For occasional outdoor use, this is a perfectly fine solution. If you’re regularly using that outlet for landscaping, holiday lights, or power tools, just spend the $15 and replace the outdoor outlet with a GFCI once and for all.