Yes you can. As I am.
But im using sdsl over a dedicated pair. In other words its not shared.
Most businesses use sdsl, as most ISP require they get it over adsl.
Cost more too.
Only thing is without a phone # its a pain in the ass to get setup.
Cause they use the phone # to see if you qualify and to measure your distance from CO etc.
You also have to have an ISP that offers that capability in your area.
When I originally ordered the sdsl service I had a phone #, the sdsl was hooked up on the other pair (telephone line).
After a few months I cancelled my phone service (already knew it wouldn't affect my dsl).
I originally went with Britsys.net and they just use NewEdge Networks.
Im am now using Vigoris.net because Britsys.net had a falling out with NewEdge Networks.
NewEdge Networks
So Yes you can get DSL service without having a phone #, but of course the phone line (medium) has to be present.
In other words Im paying for my sdsl internet connection through my ISP (which is not my phone company) and Im not paying what would be my phone company if i had phone service.