If all you're looking to do is send some kind of noisemaker over the radio to get people's attention, surely there must be a way to make that happen. I haven't used any full ASTRO or P25 dispatching equipment myself (yet..) but the system manager should be able to configure it to send a noisemaker at the dispatcher's discretion, if it's anything like Centracom Elite.
If you're looking to send and then receive/decode a tone, that's where things fall down. My understanding is that the audio compression and modulation involved in changing the signal to/from digital puts the tone value outside the tolerances permitted for a tone alert. In simpler terms, if you are generating 707.3Hz, it might come back out at the other end as 702Hz - which won't trigger the tone decoder.