Yes, Smash 4 will be competitive. By the dictionary definition of the word, it is. Especially with it's online mode.
As a traditional tournament game though, it all depends on the willingness of tournament organisers to make tournaments for the game. I also would see it as ideal if the Melee elitists didn't try to slam the game just because they feel Melee is superior when it comes out. I don't think they'll do this as badly as with Brawl (heck, even if Smash 4 was just Brawl without tripping, that'd be a huge improvement in itself). In the end, Smash 4 is looking to be totally competitively viable. It won't be as "fast" as Melee, but that doesn't make it less competitive. Characters like Rosalina, Villager, Little Mac and Mega Man seem like they will add some really interesting flair to the competitive scene. While everyone felt fast in Melee, and everyone felt a bit clunky in Brawl, Smash 4 seems to a be soild pace all around, but then characters that are supposed to be fast (like Sonic) look like they were taken out of Melee or PM, while characters like Villager seem kind of Brawl-ish in terms of the speed of their moves and their movement speed, but that is completely justified, as Villager's playstyle does not emphasise traditional, madly fast combos, but new kinds of combos that involve setting up traps. When Villager was shown in the Developer Direct at E3, he trapped a character with his shovel, jumped up to a platfrom, and dropped a bowling ball on them. This all happened within two or three seconds, but despite there being only two attacks involved, and both being at opposite ends of the time frame, Sakurai actually referred to this as a combo. This implies that it's not like Melee where you have to constantly train your reflexes and form combos that require split second decision making, but it doesn't rely to heavily on pre-determined camping strategies or anything like in Brawl, where projectile/trap users were generally better than other characters (Meta Knight and Ice Climbers being exceptions). Smash 4 seems to just emphasise both methods of play, but with different characters emphasising either method more than others, which will probably make this the most diverse Smash game yet in terms of competitively viable characters, and will make the competitive scene easier to get into for those who can't into Melee or PM.
That being said, the Bandai Namco influence is certainly there, since their fighters are like this too.