Uhm, no.
Just to be clear: The version of the GS that can't run GS OS is the ROM 0 and ROM 0 *only*. The ROM1 is perfectly capable of it; the ROM3 has a slight advantage because its ROM includes several toolbox items the ROM1's doesn't, so the ROM3 doesn't have to spend time/RAM loading those items from disk, but that's it. There are also some minor hardware improvements (they slightly modified the video system to improve performance of the IIe text modes, the keyboard controller supports StickyKeys and setting the the LED state on the Enhanced keyboards, etc) and since the mainboard includes 1MB instead of 256k of RAM it's possible to run the GS OS without a RAM card. (But realistically, if you really want to run GS OS you'll want a card anyway since 1MB is pretty much the minimal requirement for GS System 6.) But, again, a ROM 1 *CAN* run System 6, accomodate 8MB of RAM, etc, etc. Not to say the ROM3 isn't "better", it certainly is, but that's mostly because of the hardware bugfixes, not because it offers any huge functionality gains over a comparably upgraded ROM1.
Also note that the upgrade from a ROM0 to a ROM1 *is* just a ROM chip; a friend of mine ended up getting a pile of IIgs' for free, that's where my two Woz Editions came from, and every Woz in the pile had a ROM1 installed even though allegedly most of them shipped with ROM0. Apple offered the chip as a free upgrade so if you *do* happen to run across a ROM0 it's actually something of a collectors' item.
Uhm... if you say so. Yes, the 65C02 is "faster" because it can be clocked faster, but if you just swap one in place of a regular 6502 you're almost certainly not going to see a lick of difference. (If you write new code using the new 65c02 instructions/addressing modes it can be faster than the same routine restricted to 6502-only opcodes, but for existing code the 65c02 is usually either identical or, in a few edge cases, one cycle *slower* than the old CPU.)
Also it must be noted that there's a small amount of software out there that leverages "undocumented opcodes" in the original 6502: the original chip didn't trap every possible binary instruction so when it encounters a binary value that doesn't translate to a valid instruction the results can be... unpredictable, and ocassionally useful. Of the small amount of Apple II/II+ software that doesn't run on the IIc or IIe some of it fails because it employs tricks like this, or otherwise depends on quirks specific to the original MOS 6502. (Another difference between them is the BDC arithmetic instructions on the original chip are buggy; they're fixed on the 65c02, but there was software out there that used the broken instructions and breaks with the behavior change.)