Yeah, in general, this should be fine! (Of course, it'd probably be easier and less work to just use Prodigy's web-based UI if you can.)
Btw, we have a lot of users who are working with sensitive data like electronic health records and are running Prodigy on an air-gapped machine (see Med7 for instance), so I'm pretty confident that you won't have any problems there. I don't know of any case where Prodigy didn't meet the compliance requirements and it's passed every security review – mainly because it does exactly what it says it does and runs entirely offline on your own hardware 