The moment Gotenks first turned SSJ...

[OWmyDragonBallz]

Goku stated that Gotenks would be ready to fight Fat Boo in 2 full days. Well, Gotenks went SSJ and fused a day earlier. Could that be why Piccolo was still hesitant? I don't think it was said that Gotenks was ready to fight at that particular moment. He still needed more training I would assume until the second day had passed.

[Lionel]

Gotenks was already a force to be reckoned with during the transformation on the first day, was he not? Piccolo should have been able to ascertain the respective levels of SSJ Gotenks and SSJ3 Goku since he registered both of their signatures. I can only assume that Piccolo didn't want to take any chances and hoped to maximise the odds of Gotenks winning.

[precita]

Gotenks was clearly cocky and thought he was strong enough to beat Buu in his base form. As we saw...he lost, and the anime even dedicated a whole episode to it.

Fused Gotenks was not even as strong as Fat Buu, so much less than SSJ3 Goku. It wasn't until he turned Super Saiyan he got more powerful.

[OWmyDragonBallz]

Gotenks was already a force to be reckoned with during the transformation on the first day, was he not? Piccolo should have been able to ascertain the respective levels of SSJ Gotenks and SSJ3 Goku since he registered both of their signatures. I can only assume that Piccolo didn't want to take any chances and hoped to maximise the odds of Gotenks winning.

Yeah, even in the anime, TOEI emphasized the two days a bit more by Piccolo saying Gotenks is still not strong enough even after SSJ (despite being AT LEAST in SSJ3 league), but says he will be ready once the two days are up as Goku said.
Piccolo said increasing their strength even by a little bit will make the difference much higher. Probably due to the way how fusion multiplies their ki significantly.
But there is no doubt that SSJ Gotenks post-ROSAT > SSJ3 Goku > Fat Boo.

[Darkprince410]

Piccolo just didn't want to take any chances. As powerful as Gotenks would have been already, making him even the slightest bit stronger would make it all the more certain that he'd win over Buu. He even says as much after Gotenks returned from getting beaten in his base form.

Piccolo: “Alright, your fight with Majin Boo is 1 day from now! Until then, train as much as you can! If you get even a little bit stronger, it will be more effective when you perform Fusion. Got that, you miserable little punks?!”