What game are you alluding to there? FF VII or Splatoon? Because afaik both pushed their respective consoles to new longer term heights in terms of sales.
In any case, I can turn your argument against you: Just because you think it can't because only one game according to your data had given a console a 2 months+ sales push and think that this couldn't possibly happen again doesn't mean it can't happen again.
Splatoon. It caused a significant increase in baseline Wii U sales from its release in late May 2015 through to the remainder of the year. So, we're talking about a period of just over six months where there was an increase in sales over the previous baseline (and YoY) that appears attributable to just a single game.
FF7's effect in Japan appears less pronounced than in the U.S. The PS1 was already out for ten months in Japan before it came out in the U.S., and three separate price cuts created continuous growth, culminating in a strong holiday in 1996. While it wasn't exactly posting huge numbers for 1996 as a whole, there was still major growth over 1995, and it was already utterly outclassing the N64, which was nearly dead on arrival in Japan.
There was a spike the week FF7 came out, then a drop for two weeks, then several weeks of grow culminating in a big week in Week 13 (even bigger than FF7 week), then sales began to drop off to a much lower baseline (with a mid-year spike associated with SaGa Frontier and Derby Stallion, which were popular titles for the PS1 in Japan). The growth from weeks 8-14 (with the big spike in Week 13) doesn't appear to be associated with any other game, so that is likely due to FF7 (maybe there were stock issues that kept the early rush depressed?).
So FF7 does appear to have affected sales for about 2-3 months (a bit longer than the norm, but vastly shorter than the Splatoon boost we would see 18 years later), but by roughly around mid-spring of 1997 sales were at a baseline roughly on par to where they were in Q3 1996. December 1997 was the PS1's biggest December, but that was preceded by a price cut in November.
Meanwhile, in the U.S. the PS1 was struggling in 1996, and while price cuts did result in sales growth, it was getting beat by the N64 on through August 1997 (in fact, the N64 sold almost as much in just 14 weeks of 1996 as the PS1 did that entire year). Then FF7 was released in September, the PS1 experienced a huge jump in sales and completely left the N64 in the dust. In the 4-month period of Sept.-Dec. 1997, the PS1 nearly doubled its lifetime sales in the U.S., and it retained significant momentum on throughout 1998 (with the latter third of 1998 getting a boost from a price cut. There was nothing else besides FF7 that could explain that huge increase in sales and radical shift in market share. So, FF7 was absolutely instrumental in pushing the PS1 into the forefront in the U.S. That was an extremely unusual situation there, and nothing has ever replicated the FF7 effect in the U.S.
Individual games producing long-term hardware growth is just such an extremely rare phenomenon that I am absolutely skeptical that Animal Crossing could have had the same effect. With the way stock is in Japan, we may never know if it could have done what Splatoon did; sales later in the year once stock isn't an issue may give some indication, but it could be damn near impossible to tell if any growth is attributable directly to AC. In the U.S., the COVID-19 effect is clearly the predominant factor, at least for April & May. That doesn't mean AC couldn't have been just the third game ever to affect baseline sales in the long term, but you can't prove a negative.
With the available data on hand, the only proper answers to whether AC could have had a long-term effect on sales is "We don't know" for Japan and "Most likely not" for the U.S.