Connecting To Internal SATA

I currently have a mid 2011 Mac mini and an external HDD case with four drive bays. It's connected via USB 2.0 which can be painfully slow. The case also has esata which of course doesn't help me either.

What I was wondering is if I were to pop the mini open could I run an eSATA to SATA cable into the mini where the optical drive used to be?

Basically connecting my external drives directly to the logic board and making all my drives show up as internal. I'm just trying to gain some more speed as I transfer large files quite often.

My other option is to hope for a thunderbolt adaptor or a refresh of the mini with a USB 3.0 interface. Then I'll just upgrade the case

Thanks guys!