I don't see why not.
It might be risky at center, but we wouldn't be the first team to do it.
It's not Fisher's history. That's rather evident. His M.O. clearly has been to find vets to nail down starting jobs. Whether that's the best approach is an entirely different conversation. Could he be willing to change his spots? Sure, anything's possible. As I said, I just don't see it being a highly unlikely scenario.
Even GRob, who almost everybody and their uncle had rated as virtually walking on water last year, didn't start until what, game 4-5. In fact, wasn't GRob the first OL a Fisher led team has even drafted in Rd 1 in a month of Sundays. Or one of the VERY few, anyway. If he doesn't even like drafting them high, what makes anyone think he's going to be anxious to start them.
A lot of it may come down to how Fisher views his own job security. IF Kroenke has told him he has nothing to fear through the end of his current contract, who knows...he might take a different tack. My comment is based only on observation of Fisher's track record. But maybe I'm all wet. Maybe there's been little action in FA precisely because recent history with injury plagued and/or inefficient vet signings have made the team gunshy about signing FA's this year. And maybe the Rams are planning to go HEAVY on OL in the draft, and starting 1 or more rooks. I sure as heck wouldn't bet money on it, but it could happen.