I've been with two separate small civil firms that were acquired by multi-nationals. I never had to sign a non-compete, and by the time the employees heard about the acquisition, it was pretty much a done deal.
Neither acquisition turned out well - one closed it's doors, the other is a fraction of its former size. In bith cases, the larger firm failed to appreciate the value of a low-overhead, nible organization, and instead burdened the small company with the overhead of a large company - prestigious office, new vehicles, marketing staff, etc., - and then wondered why profitibility was down. Maybe your new employers are different. But if the buyers are bringing in new bureaucratic measures (non-compete agreements and the like) before they've even introduced themselves, they sound even worse than the companies that acquired my ex-employers. If I were in your shoes, I'd be working my network for a new job pretty hard.