Yes and no.
You can use Stack Exchange Data Explorer to run arbitrary SQL queries (read-only, of course) against any site in the network.
However, Stack Exchange uses Microsoft SQL Server which doesn't support regular expressions. The closest you'll get is some very limited pattern matching (
LIKE syntax). Even the simple regular expression you suggest can't be expressed with the limited syntax, though.
Stack Exchange does offer a few APIs that you might be able to use to do this: http://api.stackexchange.com/. I haven't looked at the API at all, so I'm not sure if it has the same limitation as the Data Explorer (or what is possible with it).
You could always query a larger, unfiltered data set from the API(s) and filter it with regular expressions on the client side (i.e. your own application).
I agree with Keelan that you should ask this at SO Meta. Data Explorer is cared for by SQL ninjas, so I'm sure they can provide a definite answer/maybe even offer to implement the feature :)