Hardly. Sanji lacked the power to even scratch Doffy, while both Luffy and Law were able to injure him, with the latter almost killing him. Luffy and Law are heads and shoulders ahead of Sanji. But anyways:
How does not using his Bamboo stick not make a difference? His bamboo is one of his major weapons, which is why he has the nickname Demon Bamboo. Taking away Vergo's bamboo would be the same as taking away a swordsman's sword, or Sanji's legs.
The only thing Sanji was held back from using was Hell Memories and Haki. He did use Sky Walk, and he did use Diable Jambe. Him using it once isn't an excuse for anything, one usage was enough to see that it wouldn't work on Vergo, and Vergo wasn't even using Haki. Vergo didn't use Haki, his main weapon, Geppou, Shigan, or Soru, and was fighting Sanji in the area that is Sanji's expertise, but not his own. Sanji was injured yes, but not fatigued. Protecting G5 and Tashigi would actually make him fight even harder, and Hell Memories wouldn't have even done anything to them if he had used it. That part makes absolutely no sense.
While Sanji was injured, the fact remains that he was fighting much harder than Vergo was, as Sanji held back two things while fighting in his expertise while Vergo held back five components of his fighting style, and was doing so in an area he doesn't even specialize in while Sanji does. The portrayal could not be more obvious.