A pagefile will never increase performance, but it doesn't necessarily degrade it either (with proper memory management). Running without a pagefile, however, will only tend to increase your system's instability with respect to applications requesting memory that is not available for use.
Unless your OS is particularly bad at memory management, a pagefile with 6GiB of memory should see little use. That isn't to say it won't see any use at all; IIRC MS Windows is a bit crazy when it comes to paging things out even when there is plenty of memory available. (Why, I'll never know.)
However, what happens when you don't have the pagefile in use may be reason enough to enable it: hard crashes. Most apps expect to receive the memory they request. When they don't, they crash. (Ah, but the good-old-days of having to live in a few thousand bytes are gone..., and for all too many developers, so has the practice of dealing with memory management.)
If an app is built right, it'll fail nicely. (With luck, it'll not fail at all. But don't count on it.) With most apps, you'll have a fantastic failure on your hands. Furthermore, the more apps you have that come close to that limit, the more likely you are to see system-wide instability.
Case from my own experience. Windows XP, 4GiB, No page file. Perf was great. Until we started getting close to the 4GiB limit. Then things went nuts: apps would crash, menu items would only partially appear (or not at all), buttons would do nothing, etc. I switched back to the page file, even though performance was worse with it -- overall stability was simply better and more important.
Now, perhaps you don't use any apps or do work in your apps that would push 6GiB, but I can think of a few situations where you might get close: video editing, photography editing, audio mixing and production, etc. -- essentially anything where you are dealing with a lot of data (either working with, or streaming). When that data exceeds your memory capabilities, chances will be good that your app will just go "poof".