Yes, it’s possible. WordPress uses a relational database and you’re free to add tables to it. As a warning – you will need to create new functions/classes to work with your new tables. WordPress’ built in functions will probably not work with new tables.
As a side note, new content types such as reports and tickets can be encapsulated in Custom Post Types. With CPTs you have built in WordPress functions at your disposal and it’s easy to create an admin section for your new CPT.
I’ve done both, adding custom tables and using CPTs for new content types. I find using CPTs a lot more convenient and productive most of the time.