Probably not much. I worked retail at the time, and not a whole lot of people were turned off by the need to buy a memory card. I think the cheapest one was like 20 bucks, which was all you needed if you didn't plan on going digital.
Also, the PSP kind of had a proprietary memory card too. It ran on a memory stick or whatever they called it, and unless you owned a Sony camera, you likely didn't have one lying around. You didn't need one to save I don't think, but it's still the same issue.
Vita just didn't have a lot of system selling games. Dropping the price by 20-40 bucks wasn't going to save it.