Absolutely this can be DONE! Anything they can put in there, you can take out or replace.
You will need to get a replacement drive, and you can either get one the is exactly like it, or go to newegg and look around there for a while and pick out a dvd burner. Then you will need to crack that laptop open. Generally, there are a bunch of screws on the bottom that you will want to remove, and remember/mark where each one goes, it is not uncommon for companies to use multiple differently sized screws. Once you have all the screws removed, you should be able to pull off the bottom. If you can't or it is taking a lot of force to do it. STOP. Now, check around the keyboard/trackpad (hereafter referred to as the top) and see if there are any screws there, if so, remove them again marking the placement. Now try to remove the bottom, or the top of the laptop. In theory it will go much smoother. From what I ahve heard, Vaios are an absolute bear to take apart, so good luck.