I'm implementing an algorithm into my Python web application, and it includes doing some (possibly) large clustering and matrix calculations. I've seen that Python can use C/C++ libraries, and thought that it might be a good idea to utilize this to speed things up. 
First: Are there any reasons not to, or anything I should keep in mind while doing this?
Second: I have some reluctance against connecting C to MySQL (where I would get the data the calculations). Is this in any way justified?
Not the answer you expected, but i have been down that road and advise KISS:

First make it work in the most simple way possible.
Only than look into speeding things up later / complicating the design.

There are lots of other ways to phrase this such as "do not fix hypothetical problems unless resources are unlimited".
Using C/C++ for heavy calculations in Python (Also MySQL)