Not sure about a day, but NCAA players signing very quickly after their season has finished is very common. Knies last season, Copp for us, usually a couple every year. Teams use burning a year of ELC as leverage.
Copp is the only one I remember. His last game was March 21st. I think it took him a week to sign with the jets.
@KingBogo
Edit: confirmed the dates. - took a full week. Signed on the 28th.
The recent example of it taking much longer would be Gautier - he wanted to sign with phill last March - team said no. And well, the rest is history.
Not sure about Knies.
Edit 2: knies last game was April 8, signed April 9. So it happens. I imagine there was a rush to get him in the line up as the leafs wanted to play him. Could depend on how late mcgroarty goes and how bad jets want to play him. If at all.