Can they? Well, they'd sure like it if you signed. I'll guarantee you that their agreement is entirely to their benefit, and not to yours. This happened to me once, back in the halcyon days of the 1990's. The company I worked for (a small-to-middling size contracting firm in the wilds of northern Ohio) was being sold to a large-ish national contracting firm who wanted us all to sign their non-compete. I liked the agreement I had with the local firm and wanted to keep it, but knew that if I said anything like that I'd be told "Nope, you gotta sign the new company's agreement". So I did what anyone does in a situation like this - I punted. "Gee", said I, "I'll be happy to sign this...just as soon as I have my attorney take a look at it". I wasn't refusing - I was just saying I wanted my legal adviser to look at a legal document prior to signing it, which is entirely within my rights to do. The harried administrative guy didn't even bat an eye - he just said, "Fine, sure, sign it and get it back to the office as soon as you can, OK?". I assured him I would, we shook hands, and neither of us ever saw the other again. I did actually take the agreement to my attorney, whose comment on it was, "Well, it's interesting to see they've re-legalized slavery...". I asked him whether or not I should sign it, and he asked, "Will they fire you if you don't sign?". I told him I didn't figure they were likely to do so, as it'd mean they'd get no revenue from having me work for them, so he said, "Don't sign it, don't say anything, and see what happens". I never signed it. Nobody ever asked me about it in the eight to ten years I remained with that company. Nobody knew, and nobody cared.
IANAL, and this is not legal advice. But you might consider telling them that your attorney has to look it over, and then...do whatever your attorney tells you to do, based on the document in front of you and your situation.