I'm unconvinced PS2 would surpass Wii in sales in this scenario.
Why? The content, feature, brand, appeal, competitive, and longevity advantages the PS2 enjoyed would all be gone.
Starting with competitive and longevity. Part of the reason PS2 did as well as it did was the extraordinarily long runway it had more or less competition free, it could soar a lot higher and further than its contemporaries; the NES also kept selling highly after the beginning of the next generation, selling higher than any console until the PSX and GBC/Pokemon era of Gameboy. The Gamecube and Xbox were just imitation brands of PS2 and weren't real competition. The PS2 was the genuine article, that's what most people are going to be looking at. Without that obstacle free runway where the PS2 is entrenching itself as the console to get, it's hard to justify the PS2 as taking off even close to what it achieved. So already, we have a much lower number of potential purchases because the length of time it will be selling for will be reduced by years.
Feature and brand advantage: The PS2 also had some novel features inside it, notably DVD playback. But the Wii would have trounced it. On top of that, the PS2 lacked the compelling features of the Xbox 360 and PS3, which was the extreme processing power, meaning that consideration in the Wii vs 360 vs PS3 generation would have been erased, giving the Wii a larger advantage in the PS2 generation than it had during the actual Wii generation. There were also digital features, such as digital distribution of software, communications, online play, the channels which had both information and interactive centers → having access to features like "Nintendo Week" would have been a big deal for marketing. The Wii was also a major hub for video-playback, mainly Netflix, which wasn't around at the time of its launch. Should there be an alternative to that, the Wii would make PS2's most novel feature obsolescent. And this is on top of the motion controls, which, at the time were the advantage arcades had over home consoles, at least, not for a decent price (extra peripherals required) or with great support - often, only a few games took advantage of motion and pointer/light gun features, but the Wii had that built into its base hardware with most new games and its OS taking advantage. Communication support (WiiConnect24) would have included the Miis, which were an even more appealing thing at the time with games like The Sims using such features to help it become a top game. And while Sony was entering its second generation, and the N64 & Gamecube generation weren't particularly popular, there was still a strong nostalgia bias toward NES and SNES, which would allow Nintendo to heavily leverage in ways they failed to on the Gamecube.
Content was more than just a wider brick and mortar retail library than Gamecube. It also had digital access to Nintendo, Sega, and NEC's catalogues, along with original digital games on WiiWare. These were generally a lot cheaper than retail games. Price of software was a major advantage PSX had over N64; so, rather than merely attempting to equalize it with the Gamecube (equal prices, but without even close to the volume of software), the Wii would have flipped the table on that. There is also the strong possibility that Nintendo wouldn't have necessarily lost Rare for such a cheap price, or had DMA rebel if they knew the Wii was on the horizon... possibly, this is up for debate. But can you imagine if Nintendo strengthened ties with DMA and got GTA3, GTA:VC, and GTA:SA exclusive? That's a whole other debate. I don't think Wii would exist with Yamauchi at the helm, and without Yamauchi at the helm, DMA would still be with Nintendo... in fact, get him out early enough, and Iwata in, and Square, Enix, Capcom, Konami, and others would have likely stuck around as well. That's a substantial advantage for Nintendo over Sony if all things fire correctly here, and still an advantage over Sony if they didn't.
And the appeal advantage, which really hammered Nintendo at the time of PS2 vs Gamecube. This decline in appeal began when Nintendo decided to use green blood in games, and while N64 was able to shake a lot of that off, the Gamecube buried them... The cube was seen as a children's console, given its purple colour, lunchbox form, and 80s Fisher-Price looking controller, and the flagship content (Mario with a squirt gun and Celda). Replace that with the Wii, which had a sleek and modern look that appealed to a much wider audience... ironically, despite not being explicitly aimed at children, the Wii did significantly better in that demographic than the cube did.
Overall, there are a lot of ways that Wii would trounce the PS2 should they have gone up side to side because the Wii would have likely been the dominant trendsetter for that era instead of the PS2. It might not have been as the PS2 was in the real timeline, but that lack of dominance would hurt the PS2 tremendously, more than just 20-30M. Even Nintendo fans often fail to recognize just how many more advantages the Wii had over the PS2 generation, and how profound an impact on gaming history the Wii would have had it released years earlier than it did.