IP is just the protocol used to move packets over the internet. Lots of things "move" over the internet that aren't "on the web". Many businesses use tunneling to provide "virtual private networks" that piggyback on the "public" internet.
Yes, if they aren't encrypted, a good packet sniffer might be able to capture enough of them to put the packets back together. But to do that, you have to have access to a server where the packets are routed - that usually means (1) being a sysadmin on the server in question and (2) the packets actually go through that system. Basically, that means (here in Tulsa, anyway) you either have to have access to the NOC at Level(3) or at SWB/AT&T or on the server at the dispatch center (on either end). Otherwise, you may not get the packets you're looking for as they may take multiple different routes between points.
Of course, even IF you had said access - it would still be illegal unless you were the sysadmin at the end point (even admins at the waypoints on the network aren't supposed to snoop on VPN traffic except in very unusual circumstances).
At either end of the VPN, the VOIP traffic goes through a computer and gets turned back into digital, and then (in the sound card) analog speech. One of those computers may (usually is) hooked directly to the radio.
For example, the "dispatcher" could be at a call center in India. Skype or Vonage (or a private VPN) handles the VOIP from caller to dispatcher, and a second VPN channel handles the VOIP traffic from the call center back to the radio in Owasso. The computer in Owasso could be a box (no monitor even) hard-wired to the repeater at the tower site. The traffic from there to the field unit (ambulance, etc.) is "normal" radio to and from. The repeater receives the truck's transmissions and feeds it as analog audio to the computer's sound card. The sound card does the A to D conversion, the computer breaks it into packets, gives them IP routing addresses, and puts it on the VPN for sending back to the call center. It doesn't matter if the "dispatcher" is in Owasso, Tulsa, Chicago, or Mumbai - except for the latency and dropped packets.... or the jerk that hits the fiber line with a backhoe.... or the cleaning crew that unplugs the router to plug in the vacuum.... or.....