yes, you can install on a 2nd drive. It will probably show as your "e" drive - just change the destination when you install (may need to go to "custom" depending on the software). I do this all the time.
There shouldn't be a performance hit, in fact if the HDD is faster than the 300 you may see things faster (2 drives, less contention, denser storage is faster, etc). For better results, make a 2-300GB partition to start with, this will let you use the other chunk of your drive 1st