Is it possible to sign FAs in regular season even though it would mean that your roster would be temporarily over the 53 man limit? Would you not get an admin notice to cut the roster to 53 by next sim rollover?

If you go over on roster size, then yes you have till the next week to cut players to make it back to the 53. I.e. you sing player x. midweek. you must cut player y before the game that week or the AI will cut one for you.

You would want to sign the FA during the midweek spin. Then you will have until the next spin (gameday) to get to 53 without penalty. If you sign them during the gameday spin, you will have to make arrangements to get to 53 before the sim plays, or you will lose a guy. Therefore, it could be tricky if you cut a guy and don't get the FA. You would play the game with only 52 rostered.

Ah ha, thats it! Thanks.
Why I'm asking this is just as you say, I put offers in which were accepted only to get released immediately , quicker than Anthony Barr visiting the Jets !

Remember the waiver wire runs every midweek. If you do free agents then, you'll have until the next game to get your roster back under 53. If you don't get it under, the AI will do it for you. If you press the "cut" button on the player card, the sim will process the cuts before it takes you behind the woodshed. Your pending cuts will show up under the "Pending Contracts" section of the My Team menu.