As far as I'm aware, as long as there is a squad place available (or you request a registered player to be removed to make space) you can register a free agent at any time outside of the transfer window.
I found the following for the EFL and I'm presuming other leagues follow similar principles. They do have to make the request but I can't see why they would refuse.
The League will only consider granting permission to make changes to the Squad List outside of a Transfer Window where:
- the Club’s current Squad List contains less than the maximum number of Players permitted to be included on the Squad List and the Club wishes to add an Out of Registration Player or another Player registered with the Club but not currently included on the Squad List, or
- in other truly exceptional circumstances.
My understanding is, you can add a free agent player to your team at any point. But they can't play in the league or various competitions unleas registered to play in that competition prior to the deadline. They can only train with the team.
I think I thought the same as you previously but someone had convincing precedents otherwise.