mbachur-
I am positive that this is paskened in th SA though I don’t have the source offhand, but I’ll look it up when I get a chance unless someone else here knows what I’m talking about and gets it first.
Agav, I disagree with you; if there is a halacha in the gemara that no one argues with, even if the SA doesn’t mention it, as a general rule every single rishon and acharon will tell you that it is the halacha and no one will argue on it.