I have done this with both T-SQL and PL/SQL. The stored code is all available in system views and easily extracted with a script. If you set up the script to run automatically at a given time, you know that the version in git is at most n hours out of date. If you leave the control up to the scheduled job, then your commit messages may not be what you want. But there's nothing keeping you from running your extraction script off schedule and then writing a good commit message.