Yes, it is possible.
My last job was customer service - I worked in collections but my customer service skills had me promoted to a customer service specialist within the office. I find using a telephone very difficult, but being scripted helps a lot because you don't have to worry about how to carry out a real conversation, once you've been in the job for a while you know enough to give answers and direct the call so it takes out a lot of the anxiety about the unexpected. It was a challenge, the first call was tough, and the sort of culture in such work places tends to be a less than great one for aspies, but it is possible to work in that sort of role as an aspie.
I lost my last job mostly down to management wanting me out and the company not wanting to have to pay me redundancy - I've been on a work placement in a call centre since then but between the company being dodgy as hell and my anxiety about making calls again resulted in my having a meltdown. Currently it's close to impossible for me to use a telephone, so I'd not be able to work in a call centre again right now - my point to you is that it's possible, but if you're symptoms are bad it may be a problem for you. If you're considering applying then chances are that you are capable, don't let any doubt creep in - and good luck!
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Bloodheart
Good-looking girls break hearts, and goodhearted girls mend them.