If I turn off wireless on my computer but am plugged into a wireless router, can I be hacked into wireless-ly?

You could be hacked by someone who is connected to the wireless, yes. All devices connected to the router either wired or wireless are on the same LAN so it doesn't matter how you connect.

So you would be hacked through the Ethernet not the wireless but the hacker could be connected either way and accomplish the same thing.