I once tried to get a job as a messenger in London and a lot of the companies I spoke to wouldn't allow you to ride brakeless. You didn't have to use the brake, it just had to be on your bike. This was for liability issues they claimed.

The only other bike issue I've ever come across was some more specialized messenger companies (Pedal Express comes to mind) may require you to haul a trailer. Obviously most track bikes aren't suited to that. But I've seen people do it.

It really shouldn't matter what you ride as long as you can get the job done.