No, they won't.
Strictly speaking to the football aspect of this, the Steelers should absolutely just move on from Bell. The kind of money he is asking for is insane for a running back no matter how good he might be. The prime of an NFL running back's career is easily the shortest when compared to all the other positions. If the player is consistent he may stick around with the team for 4-7 years before you see a decline simply because the player's bodies just can't hold up. Just look at a guy like Eddy Lacey. He had two really solid years for the Packers, got a toe injury, gained some weight and two seasons later he's out of the league.
It just isn't worth it in terms of the possible money risk. If Bell is asking for a bunch of guaranteed money and (hopefully doesn't) has a career-altering injury which makes him a lesser player, then Pittsburgh just wasted a bunch of money. Another fact of the matter is that Bells production can be replaced by two running backs who can distribute the workload evenly, and not rack up all the ticky tacky injuries. But Steelers already found a viable option and his name is James Connor.
James Conner || 2018-2019 Mid Season Highlights ᴴᴰ YouTube
So far this season Connor has put up numbers that even surpassed Bells. Connor has rushed for over 10 touchdowns, a feat that Bell hasn't done in any of his previous seasons. He's averaging the same amount of yards per game as Bell has for his entire career. And the best part is Connor is under contract for the next two seasons. Now instead of paying Bell like he's a quarterback, they can have Connor for the next couple of seasons getting paid like a mid-round pick.
Probably the biggest reason why Pittsburgh should move on is that of the harm his holdout has done to the relationships he had with his teammates. Multiple members of his offensive line have spoken out about their dislike of his holdout and most insinuating that he's only in it for the money.
The Steelers are known to be a franchise based around emotions and this could be the downfall of them. Football is the ultimate team sport and if all 11 guys don't all trust each other nothing is going to work. It's probably for the best that both parties just go their separate ways with this one.