Personally, I throw any database calls into try/catch blocks, because there's always the potential for issues to arise. You'll want to set some default values in the catch block, and if it happens to land on these defaults for whatever reason, display the end user some sort of (ideally pretty) error message.
Running a SQL query isn't always guaranteed to pull back any sort of results either...any number of things could go wrong - the server could be down, the connection could be so saturated that it's not able to pull the results in a timely manner, it could be sitting in the dead center of a backup of sorts too....These things have to always be accounted for, that's why I recommend doing it the way described above.
Lastly, to answer your question, yes, JDBC will in fact throw an error - under any of these circumstances.