Okay...you need the 9bu024e for the Drake II. And what you showed us a picture of was that, correct? And you didn't get that, but instead got the weird-looking 9bu004e, which is THIS am I following? (Actually, I see now another picture of a different gasket with the 004e number on it as well, but I see the difference.)
The weird-looking one is the old Drake tank to bowl gasket, 9bu004e, which has been discontinued. Both the Drake and the Drake II now use the same tank-to-bowl gasket, the 9bu024e.
So if I understand, you are asking if you can use the old gasket for the original Drake on your new Drake II, where both the Drake II and the Drake now use the same new-model gasket. (Actually, looking at my spreadsheet, almost all the Toto 2-pieces with standard 3" flush valves now use the newer 9bu024e.)
Your specific question is, "Will it fit?" Well, yeah. I think it will. (The smartass answer, of course, is, "I dunno, does it?", because you have the toilet and the gasket right there. But I understand that you are, I think, really asking if there's anything wrong with using it, i.e. will it break something.) I looked at my handy-dandy spreadsheet with all the part numbers for all the toilets, but they don't show obsolete tank-to-bowl numbers on it, and I can't find a Gwyneth parts manual prior to March 2008, which even then shows the 024e as the part you want.
So I don't see anything that would let me tell you that there's absolutely no problem with using it. If I needed it right now, I might just try it very carefully, because I'm an experimenter.
If I could wait one day, I would call Toto customer service in the morning at the toll-free number on their web site and ask them. If I could wait two days, there are plenty of places selling it online, including Toto, who will sell it to you for $4, and they're pretty quick to get stuff out the door and don't kill you on the shipping, usually. And they might send it to you for free if the original one was defective (Didn't you just buy this thing? If it wasn't in the box or was damaged, they'll almost certainly mail you a new one for free if you call 1-888-295-8134 and ask. They're very nice.) Also, I can't imagine that there isn't a plumbing supply in DFW that doesn't have these in bulk.
I know this isn't all that helpful...sorry. Maybe Terry will see this, because he is almost certain to know the definitive answer.