It's doable but it would be custom firmware and it's not really necessary. Two way paging isn't really worth doing because then you need a massive device with a massive battery, or something that uses uncontrolled mobile phone networks (and generally still has a massive battery, that lasts about a day).

You wouldn't even need particularly good encryption, you'd just need something adequate to stop casual eavesdropping really - "keep them busy for half an hour" would stop people from sniffing the POCSAG traffic and tweeting it, so that people show up at incidents and hang around filming it on their phones.

This incidentally is what a guy in England got arrested for a few years ago, exactly that. It's perfectly legal to listen to and decode pager messages (or any other radio messages), you're just not allowed to pass them on to people or act upon them, and posting them on twitter and then going round to rubberneck at the ongoing incident very much ticks those boxes. As with so many things in the UK, to paraphrase Aleister Crowley, "Don't Be A Dick shall be the whole of the law".