No. They are transmitted on separate virtual pipes, not separate physical pipes. Those dishes you see on cell towers have physical limits, and that's the only real pipe. Voice calls and Freeping are each taking a slice of that real pie.
Interesting story: One of the physical limits that exists is power, and you can increase the size of the "real" pipe by turning up the juice (but only to a point). There was a security guard who regularly set up a lawn chair adjecent to one of he large dishes on the ground. The microwave transmissions would warm him in the Canadian Winter. Well, he did it on Christmas day like he'd always done, but he didn't know they had cranked up the power to accommodate the anticipated Christmas phone traffic. You can guess how that one ended.
Question then: The spectrum utilization itself is the component of the pipe, correct? Meaning you're either using a channel or you're not. Today's modern smartphones maintain an always-on data connection for things like push email, etc., which would tie up a data connection 24/7, normally.
If that's all true, then what's the difference if I'm browsing low-bandwidth FR vs. high-bandwidth HD video (other than the theoretical throughput capacity of the cell site)? Both occupy the already-used connection to the cell tower for data. Voice would therefore be independent of this, and not suffer whatsoever in high bandwidth data vs. low bandwidth data.
Maybe my premise is wrong and high-bandwidth internet traffic consumes more of the spectrum, but I can't see justification of that anywhere on the net. I'll stand corrected if it does, however.