I seem to remember some of the Woz editions shipped with ROM 01 boards. It looks like mine certainly did.
Also, are there any real hardware differences between ROM 00 and 01 machines? If not you should be able to upgrade just by burning/swapping in an 01 ROM.

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From memory, I think that Dog Cow is mostly right. However there were some non-ROM differences between the 00 and 01 boards -- ADB and timing corrections? Most of the time, applications will not notice the difference.

My Woz IIgs came from an enthusiast who ran the latest and greatest stuff on it. It boots up to declare itself as a ROM 01, but like most like it, it's an original board with ROM swap.