the research indicates it advances speech - IF you use the word alongside the sign. just using the sign doesn't seem to confer any benefit. the signs need to be used regularly and in context for maximum benefit. (crais et al, 2009, a macro review of the research). it's the difference between attending a class once a week, and LO hopefully 'picking up' a sign or three, and using the signs consistently at home.
one of the reasons it's suggested it advances speech is because child learns effective communication sooner, and is more motivated to use the words, too. eventually most use just the sign (often alongside a vocalisation such as a grunt or babble), then the sign and the word, and then the word only.
babies can use signs to represent objects (cat, dog, milk) from about 6-8 months, whereas the corresponding holophrastic verbal phase isn't usually until about 9-18 months. similarly, representational signs (love, pain, anger, loss) can be used from about 12 months, with the corresponding verbal equivalents varying depending on the child and their experiences, but not usually before about 18 months. a child who has solid signs at 14 months will usually perform significantly better than his non signing peers at both 24 and 42 month verbal and comprehension assessments.
have seen amazing things with sign, especially when children get to 8/9 months and their comprehension is way ahead of their verbal competencies. as long as their motor control is good enough, they can get their message across tantrum free.
however, with all of these things, the key word is usually.
doesn't work for everyone though. in the same way some children will refuse to use words long after they're capable (with or without sign language training) and then will suddenly burst forth in telegraphic or even complex speech, some will refuse to use signs full stop.
worth trying - i've been using some starter signs (mummy, daddy, milk, cat, nappy) with my baby from birth, and from next week she's at tiny talk.
https://www.handyexpressions.co.uk/baby-signs/family-signs.html has some good illustrations.