Can you provide support via twitter?

Can you? Yes, certainly.

Should you? Most likely not.

Unless you have a very new, or wildly successful widget, support via Twitter is likely to be more frustrating than beneficial. It's a little like trying to get investment advice by talking to someone on the NYSE trading floor...

At first I thought "No", but now I'm leaning toward "maybe". If you can't reply in 140 characters, provide a link to more info. If you get the same question over and over, add it to your FAQ and tweet the link so that all your followers can see. It may be tough to keep up with it all, but if your customers know you are listening, they will keep the feedback coming.

Not really, 140 is pretty limiting. You should be using it as proactive/preemptive support. Grab up some rss feeds of some searches pertaining to your service/startup and D or @ respond to people who bitch when something not right.