The hard drive on my Sony Vaio recently took a dump, I've concluded that the only thing I can do is replace it, my question is will I be able to still watch blu-rays on it if I just download the drivers off the Sony website or will i need the recovery disc?
When you purchase a new hard drive it contains no information on it. To answer your question, yes you are going to need the recovery discs. Using the recovery discs it will bring your computer back to factory condition (software wise) meaning all the little programs, trials and whatnot that sony put on there will be back.
Also all of your data is not going to be on the new drive.
And also the recovery discs will have the drivers on them, but they may be outdated. So you can either update them from sony's website or just run windows updates.