Definitely.

I don't know what you should charge, but I guess you could gauge it off of what they are allowed to loot. Say I wanted Timbal's for my warlock, I'd pay you 50ish gold per run to get it, or a bulk deal of something like 200-500 depending on my current gold situation. I'm sure demand will be high enough for you to be picky and charge a lot for runs though. 10 gold per badge? 20 gold per badge? I the service was fast and easy, I could see people paying that much and probably more for the rich and lazy.

I'd start off by recording a fast run with your team of 4 and posting it on the server forums so that they can see you're the real deal. Then post in that same topic that you plan to sell HC runs for X amount of gold and item/badge runs are negotiable.