Is it possible to send Emails to different departments, depending on what a user selects?
Yes, it is.
In QuickMode, in the Select-List element's Advanced tab, there is a "Mailback" checkbox. If you check it, the values of your select-list items will be used as Email addresses to send the "Form record received" Email.
The List would look something like this:
0;Bug;firstname.lastname@example.org 0;Information;email@example.com 0;Sales;firstname.lastname@example.org
If you have an Email cloaking plugin, make sure that you put it BELOW the BreezingForms plugin, otherwise it might not work correctly.