Yes, not correctly disposing of special purpose objects such as DB connections or graphic contexts causes memory "leaks" and may also "leak" system resources such as file handles, DB connections, etc. - it is up to you the programmer to correctly handle these special objects.
It is more likely that you would run into mysterious failures but out of memory exceptions are also possible.
In answer to another thread of yours (see below for link) I mentioned that the jamon jdbc driver will time your sql statements. It will also allow you to see how many connections you have open, and a number of other things such as how many SQL exceptions have been thrown. You can also view the stack traces via jamon.