Not at all a dealbreaker, no - if you're buying the systems, it makes sense to buy what you are able to afford and support the best.
I was more responding negatively to the idea that other machines wouldn't be allowed to be used in development at all (personal machines, for instance, which almost every person worth hiring will have at least one of, and in many cases, which they'll vastly prefer to use), but I re-read, and realize that you mentioned security concerns. That changes matters quite a bit, assuming the security issues are really important (having an internally-perceived killer app and worrying about it getting out -> not necessarily very important; working in an industry where competitors regularly steal trade secrets [finance and gambling, for instance], or where regulations/investors demand tight security, -> important!); I would usually be annoyed if I was not allowed to use my personal machine for dev, but if there are legit security requirements, it's a lot more understandable, and I wouldn't have any problems at all using a standardized stack.
Honestly, from my point of view I'd be fine with any OS restriction that's not Windows. It sounds like OS X is not a real option for the work that you need people to do, so it's perfectly reasonable to insist on Linux, and the Thinkpads are very nice machines (I actually quite like the "nub" for mouse control), so I don't think you'll hear too many complaints if you offer them.