Fix your pluggin ....otherwise you're gonna have lots of trouble. Especially if you need to use Odin.
But yes, if you're rooted and have a custom recovery already...you should be able to flash roms. Just not stock...that requires Odin....and you wouldn't be able to root again after even if you could flash stock. Also...depending on you're recovery version.....you may need a different recovery version for different android versions.
You gotta fix your port. How do you charge the phone? If you run into issues and need to flash stock with Odin....you'll be out of luck. You need that port working.
Sent from my Moto X cellular telephone...