The PlayStation Mobile website says that the HTC One V will get PlayStion Mobile:
PlayStation®Mobile for Android™ support on HTC phones is rolling out with Android 4.1 and above upgrades, timing of which is subject to regional and operator circumstances.
Ok, here's the problem. HTC says that the HTC One V will not get 4.1 (or 4.2) because it doesn't have enough memory. So... With that being the case, will it get PlayStation Mobile or not?
Wikipedia says it's upgradeable to 4.1, so it would probably work then. That might be the problem I'm having as well. I just got the HTC One S and read that it works with PSM, but when I try to launch the app it always gives error 8008103E. I'm not sure how to upgrade or if it's available yet. It's not very important to me but I wanted to try it out, and I'd be more likely to buy an app that I could play on 2 devices.
Edit: That does seem to be the issue for me. I found on another page:
For the HTC One V: "Details to be announced later on."
For the HTC One S: "Please update your firmware to Android™4.1 or above. For how to update, please contact HTC's "Customer Service & Product Support" in the country/area you are using the device in."
It looks like the update for the One S will be coming this month, so very soon. I did not contact HTC, but that's what Google searches suggest, and related phones are have been updated in the past few days. Unfortunately, it looks like the One V actually won't receive the OS update, so it may work but will probably depend on something else.