Somewhat I suppose on the surface, but if you break it down, you'll see the '01 Aurora went up against the TL, ES, I30; the LeSabre/Park Avenue took on the Grand Marquis, LHS, Concorde; and the Bonneville challenged the 300M and Intrepid.
They were also far more specialized, with the LeSabre/Park Ave having softer rides, styling, and bench/column shift options, the Bonneville being very American and muscley, and the Aurora simply occupying a higher plane.
Now, there was certainly overlap within the lines, like Bonneville SE vs. LeSabre Custom and pretty much LeSabre and Park Avenue, but as a whole, I don't see it. The Bonneville's biggest problem seemed to be the Grand Prix, though the Bonnie was far more refined, Pontiac buyers simply don't care; I believe a V8 offering for the 2000 model year would've been a big boon to sales.
Right now, I don't see that much seperating the Avalon from any of the other two it shares underpinnings with. Its not that luxurious in comparison to the new Camry, the power output is the same, the trunk is larger by like a cu. ft., the Camry also has reclining rear seats as an option, and they got rid of the senior-tailored 6-seat/column shift option that won over people in 2000. All three are also conservatively styled, bordering on luxurious and now the Avalon seems the least 'pricey' of them all. Generally, the large car market doesn't exist anymore and the Avalon seems to be there for the sake of being there.
Again, you're right; we'll see. But I think the Avalon's numbers were artificially boosted by the wow factor of the first year and that it went unchallenged within Toyota for almost two whole years. I don't see why they just don't import a decontented Crown with a bench seat. I bet you'd sell out the whole shipment with vinyl tops and vogue tires.