From the application layer? I don't believe so outside of the phone's native dialer/closed source firmware.
>If I'm reading things right, it implies that IMS (eg modern SMS/MMS running over IP) actually uses a different data channel that gets a higher priority?
I believe all IMS traffic is going to be higher priority regardless of if that's voice or SMS. They're both carrier-provided SIP messaging so if SMS over IMS is configured, it would use the same APN, go through the same CSCFs, and get priority. It's all the same PHY connection though. There's not a fully separate set of wireless channels for voice and data like it was in the CDMA standard where there were CDMA carriers for voice and EVDO carriers for 3G data.
You wouldn't be able to just host your own SMS though. You'd need a private APN from the network operator to do anything like that. Other systems hosted by the operator (HSS and MME) are what allow you onto the network.