Its definitely possible. The key to getting signed that way is having mutual friends who can vouch for you before you walk in the door and a business that has room for an undeveloped artist. J.Cole, I would say had a similar story. Maybe he had a huge fan base in NY or NC but no one in Texas or down south this way really heard of him til news hit that he was the first artist signed to Roc Nation.
The question though is do you really want to get signed that way? First off, you have no leverage in contract negotiations since no one has a bidding war for you and since you can't eat off tour money til the money looks right. Walking looks real hard when you see all those zeros.
Also you tend to lose creative control, as well. Because you can't tell the label hey I know what I'm doing look at all my fans who love me for who I am now. I think there was an interview where J.Cole handed in his first version of the album and Jay-Z threw it away. Now if there is anyone you want judging your album its Jay. But its not like every label has an 10X platinum, Hundred Millionaire, Icon that transcends music as an executive that has time to listen to your whole non-released album. Alot of these suits follow trends and don't know music more then the artists on there label and yet there the ones that will throw away your first album.
Three they make your image for you. If you depend on the label marketing you then they will market you in the least confrontational way possible. And you'll look like the boy scout of hip hop so that you can appeal to soccer moms and junior high kids.
fourth your dependent on your label for album sales. Look at artist who have huge creative influence and completely control the marketing of an album and look at artists who built there own lane then signed or released later. Frank Ocean and Kendrick Lamar comes to mind. Both these artists are on there way to GOLD and they weren't complaining that the label wasn't promoting there singles enough or that they didnt ship enough albums.....