No Cinelli bikes had a 2-digit serial number that I can tell. Whether they ever marked BBs with the frame size is unknown to me. There are a lot of Cinelli owners here on the forum who can confirm yes or no. You might ask over on the C&V forum as many of the members don't bother with this specific area.
This website, (
https://thecinelliregistry.com/ ) shows a large number of registered Cinelli Model Bs and with a few exceptions the numbering does follow somewhat of a pattern. But like I said, there are exceptions so nothing dogmatic can be said as to where a particular number might belong in the sequence.
Still, I think it is helpful. I also think the owner of the bike should look harder to see if there is a 4-digit number on the BB or perhaps elsewhere, such a on one of the rear dropouts, etc.
Also, just found this which might be helpful.
Cinelli Head Badges:
1949 - 1958 56mm Cinelli crest paint-filled silver-plate over brass head badge
1958 - 1971 51mm Cinelli crest paint-filled silver-plate over brass head badge
1971 - 1978 Cinelli crest anodized aluminum head badge
1978 - 1979 Cinelli crest decal head badge
1979 - today Flying C decal head badge