Errr...no.
No Jr's not.
Bowser Jr is at best the same level of importance as Toad; secondary character importance.
Mario, Luigi, Peach and Bowser are of course the primary protagonists(+ damsel and antagonist)
Yoshi and Toad are secondary protagonists in the Mario series; they aid Mario and Luigi in their quest to save Peach from Bowser.
Bowser Jr. is a secondary antagonist; his job is to support Bowser in his mission. He's more important than tertiary antagonists; like his (no longer) siblings the Koopalings, but he's very much a secondary antagonist.
See you're a bit off here. Yoshi is a primary protagonist in Yoshi games, and he's also repping the Yoshi series, not Mario. He may be secondary in Mario games but not his own.
Jr. in on the cusp of becoming a major character in the series. No doubt, he'll never compare to the 4 mains, but ignoring the fact that he's been a CO-antagonist in almost every game since his release, including the platformers and recent Paper Mario games mind you, is quite foolish. He's a lot more significant that Toad.
MorbidAltruism has a point, we can't forget his Japanese popularity, however, I pose this question. A Japanese man in a Japanese compnay made him a meat shield in each Smash he's appeared in. He may be popular, but is he important enough to rep the series?
And also as for his Tingle statement because I'm too lazy to quote, I don't think Sakurai haphazardly adds characters to a franchise unless they're big in popularity AND important to the series as a whole.