Yes, they can:1) You can be asked to sign a non-compete, non-disclosure, and/or non-solicitation agreement at *any* time: they do not have to be signed at hiring. If you don't, you may be terminated: signing the agreement can be a requirment for continued employment.2) Any agreement can be backdated or have a retroactive effective date.3) Backdating doesn't even change anything: once you sign the agreement, you are bound to it, so all backdating does is make the file look more regular (like everything was done at the ideal time, at intake); it does not give the company any more rights or make the agreement any more binding on you.