It's some help, but not nearly as much as pratcising the sax, if that's what you want to play. I played classical clarinet to a pretty decent standard. No recordings available on clarinet, I'm afraid, but if you want qualifications, I got a distinction in my grade 8 at about the age of 17, and kept at it steadily for another 13 years after that, played in a few University orchestras etc. Is that some kind of standard? I don't know. Does it make my opinion worth something? not for me to say. After a twenty year break, I took up alto sax. Three or four months in, I realised I was holding myself back by trying to blow the sax as if it was a big clarinet. My saxophone embouchure is much more relaxed and oepn-jawed than my clarinet embouchure ever was and it gives me much more flexibility in terms of the sounds available to me from the instrument, which is particularly useful eg if you want to play jazz (which I do).
Playing any wind instrument will teach you basic breath control. But surely the most useful one to learn and practise on is the on you want to play?
PS I strongly suspect Nick was pretty handy on the clarinet, having listened to his sax recordings. He wouldn't accept less from himself