Is it possible to interact with an ODBC connection within AppleScript? Or must one break out into another process (e.g. Python, Perl, etc)?
AppleScript has very few built-in capabilities, and in particular, no built-in functions to talk to databases, either via ODBC or any other protocol.
What is does provide you is a way to control applications that have that ability, or cut out to system scripts that also have the ability as you suggested in your question.