The enclosure will not be overloaded, it will work fine. However, don't expect to get the full speed out of the 6Gb/s, because you won't.
It should, however, be faster than good ol' USB. You'll transferring data at a relatively standard SATA II rate (3Gb/s or less)
That's gigaBITS, not gigaBYTES. Also keep this in mind.
You really won't see any benefits with a traditional platter-based hard drive running 6Gb/s, whether internal or external. The only way you'll really be able to get most performance out of it (at the moment, anyway) is to go with a 6Gb/s SSD, which is expensive, but stupidly fast.
There are some 6Gb/s traditional Hard Drives out there that do give some performance gains, but don't expect night/day improvements. We're talking a few seconds off of load times or data transfers.
Personally, I'd save the money until SSDs become more affordable