It should void the warranty, at least on the enclosure. Not sure about the drive, if the S/N is linked somehow to the whole product, I'm sure they won't support it if it fails outside the case. Only way to know for sure is to read the product documentation or contact the vendor.
I'll tell you about my experience with a WD 1TB NAS, the MYBOOK. It has a regular cheap WD Green drive in it. Well, the device failed and was no longer accessible over the network. Obviously, I needed that near 1TB of data on the thing. I took it out of its enclosure, but it was not a simple task of simply attaching a sata cable and power and pulling the data off. I managed to save a few files using R-Studio's recovery software. I would just get the bare drive. I can't speak for Hitachi's enclosures, but the WD enclosures appear to use different firmware and made it an absolute pain to attempt the recovery. Once I got what I could off of it, I put it all back together after writing 1s about 7x to it, and returned it to Best Buy. Luckily, I had 1 day left of the manufacturer's warranty so BB authorized a simple swap for a new 1TB NAS. Point is, you'll almost always be better off with the bare drive if you should ever have the misfortune of needing to recover files from a defunct drive.