I would hazard a guess that there is no reason why you shouldn't have as many mail clients as you like on your system. If you have your mail set to delete from your suppliers 'post office' as soon as you read it (which is the way things normally work) you will probably end up with some of your mail stored in one client, and some in another.
And, depending on how you have set various defaults on your system, you may get a bit of confusion if you expect one client to pop up, but another one does...
That said, I have 14 separate clients sitting on the machine I am currently using, serving 14 different e-mail addresses, and it all seems to work smoothly...