Maybe can probably do that, but that does not mean it is a good idea.
In general, I would definitely use a try-catch-finally clause (or using) around the logic for handling a DB-Connection. Not only will this be safer for the reasons you are asking about, but it will also be clearer that things are handled well, and it will make it harder to accidentally mess something up if you should decide to change something in your GUI-layer later.
You should handle logic (and the creation and disposing of instances) of this type as close to where you need it as possible.
Note: A Finally clause will let you ensure a connection is closed, but still let any exception "bubble up" to the top, if that is what you need.