"Would there be a way to upgrade the processor or am I just being foolish with that one?"
So doing that by just swapping out the processor is not possible. However it is possible but would require changing the entire logic board to i5 or i7. I'm not sure you'd get the difference you expect and it would be difficult, not for the faint of heart, and expensive.
If you want a huge speed jump then drop an SSD in there. Yours would take an 6 G.
http://eshop.macsales.com/shop/SSD/OWC/Mercury_6G/
Here's my early 2011 13" MBP w/ 8 GB RAM and a 120 GB SSD all from OWC:
Startup
http://tinyurl.com/ooe6sac
Photoshop CS 6 startup and open job:
http://tinyurl.com/nsussol