AFAIK, all "data" starts with a GSM connection, via a Hayes-like protocol, where you send ATDT*99# and you then get a TCP/IP connection and you connect your TCP/IP stack to the modem, and you get a "socket" interface. The data rate is automatically selected. I was doing that on the Siemens / Cinterion MC52/etc modems.
The above works the same way whether it is GPRS ("2G"), EDGE (basically double speed GPRS), 3G, HSPA (basically 3G but faster), 4G or 5G.
Voice and SMS still runs over GSM. AFAIK nobody runs voice or SMS over 4G etc. although the cellular system is free to do what it likes internally, and it probably runs everything over some IP protocol.
So, no GSM, no data. But in terms of coverage, you always have GSM. You never have say 4G coverage but no GSM coverage. What you do often have is GSM and no data, or GSM and only GPRS (which is too slow for "internet" use these days since even the HTTPS certificate exchange takes too long).
I did a search and could not find out what the towers transmit continuously.