Actually I did search for "Privacy Protector" in the Play Store app on my phone, and was describing the first app returned with that name (and the only one on the first screen of results with that name).
Searching from a computer (when not logged in to Google) I did find a couple more,
the third of which sounds like the one you are talking about - the second was something for cleaning up call logs and messages, and there were many more apps with neither word in their name that were listed higher in the search results. This merely confirms two well-known facts: (1) app names are not unique, and (2) the Play Store search is not all that good.
Anyway, to answer the question: I've never used it, so can't personally comment on how well it works or how reliable it is. I can imagine that it could be a right pain if it decides that an "untrusted" app is running when you want to use the network, and I notice that you have to manually re-enable the network afterwards. Also you need to decide which apps you don't trust - if you don't know that say CM Security is untrustworthy then it won't protect you against it (and that's not a hypothetical example, Cheetah Mobile apps are a definite threat to privacy). I do note that the average review score is not all that good though.
Personally if there was an app I didn't trust then I'd not allow it on my phone in the first place, rather than mess around with stuff like this. There are always alternative apps. Of course since I'm rooted I can also run a proper firewall, which would be a better solution than this app appears to be: if there's an app I don't want to have network access I can block it while allowing others to operate normally, rather than shutting down all network connections if that app appears to be active.
Bottom line: it's up to you, but assuming I'm discussing the correct app this time, it's not a solution that would appeal to me.