Not reaaaaally, I'd say It's lacking some things that define a true 2D fighting game.
Smash bros is more like a player vs player 2D side scrolling beat-em-up or platformer by function. In fact, it shares a lot of mechanical similarities to Sakurai's early Kirby games like Super Star in terms of how it operates. This allows Smash to have a pretty different set of rules compared to a standard fighter, such as greater freedom of movement and more nuanced use of moves, but in exchange you give up a few things too.
Unless it's got a rich high/mid/low defense system, a real okizeme game, and some sort of resource management system (ex bar, that sort of thing), it's lacking some really defining traits of a 'traditional' fighter.
Saying it has a higher skill cap than a more nuanced 2D fighter that actually supports and rewards advanced, high-level play such as Melty Blood or Guilty Gear is a bit of a crock too, imo. If you can grasp spatial control and memorize the intricacies of a small handfull of moves, you can play Smash well. You don't have to worry about things like crossups or fuzzy guards in smash, and most character's moves are a lot more straightforward in terms of design than those found in your typical Arc Systems fighter. Character complexity, too, is far more advanced in those games compared to Smash. As someone who plays both Smash and traditional fighters, particularly japanese fighters and japanese imitation fighters like Skullgirls, I can say that pretty confidently.
Smash Bros is actually a lot like Outfoxies, an older game that did platforming pvp first.