At an affordable price? Probably not. The console itself was $299 in 1995.
If you're talking about the brand itself. Nintendo was already the big brand in the 80s, heck its arguable its still big now since we're getting theme parks, Mario being in the closing ceremonies of the Olympics, mobile apps, merchandise, etc. Kids and adults in the 80s and 90s would usually say "let's play the Nintendo" or "it's on the Nintendo." Mario, Zelda, Donkey Kong, Metroid, Star Fox, F-Zero, Yoshi, and Kirby became household names from the 80s to the 90s (not to mention the biggest name alongside Mario and GTA, Pokemon). Sure things have changed in the new century, but you cannot say any other franchise is bigger than Mario and Pokemon besides GTA (which is more likely due to the older teen/young adult crowd).
Let's correct one thing - Nintendo isn't getting theme parks. It's getting themed areas in 3 Universal's theme parks.
Nintendo being a big brand in the 80s did not stop sales to drop from the NES to the SNES.
And add FIFA to the list of franchises bigger than Mario and Pokemon. I'd argue that Battlefield, CoD and Elder Scrolls are also bigger. Destiny and Overwatch are potentially bigger too.
Adjusted for inflation, the PS cost about the same as the NES ($393 vs $364). There's no denying that Nintendo was massively lucky and has to thanks Atari for its gaffes.