Graf will likely want to be promised NHL games to end the season if he signs. Not sure if the Rangers or several other teams can offer that. Graf could be a New York hater additionally, he's from Massachusetts.
If Quinnipiac makes the Frozen Four (April 11/13), there'd only be a few days left in the NHL regular season. So it might depend on whether they get deep in the tournament. Typically the guys with a bunch of offers would need a few days to sort things out. He probably has narrowed it down to a handful of teams already.
I recall when Drake Caggiula won with North Dakota in 2016, it coincided with the end of the NHL regular season. So he took his time (probably a couple weeks to party with the boys) and eventually signed a month later.
They weren't undrafted, but I remember BC's Miles Wood and Steve Santini being eliminated on the Thursday of the Frozen Four. They flew back to Boston with the team and the immediately drove to New Jersey to play in the Devils season finale on the Saturday. They both expressed how that quick turnaround was a little surreal since they didn't really have time to mentally unpack.
Graf would still count as 21 if he signs in the next month, so it'd have to be a 3 year ELC. He probably has enough leverage to have the contract get registered for this season and have the first year burned. The 10 game slide rule wouldn't apply to him, so he doesn't necessarily have to suit up in an NHL game. But usually if a team has been eliminated or has its playoff seed in place, then it's customary to suit the new guy up (and give a vet the night off before the playoffs).
Since Graf wasn't on a team's reserve list prior to the deadline, he'd be ineligible for the playoffs. So he couldn't jump in a la Chris Kreider, Cale Makar, or technically Nikita Gusev (with Vegas).