GURPS takes a very "laws of physics" approach to mana. In some worlds the laws are different, so much so that magic is real.
It comes down to the way the world's meta-magic rules are designed. And often these questions don't come up in campaign settings as the characters do not often traverse world settings. I do not recall GURPS Core or Magic covering characters who travel between worlds.
If your meta-magic setting ruling say that magic is non-functional, then the outcome is simple. It does not work, because mana is one of the ingredients required and it is not present. Like trying to make a cake without a key ingredient.
If the ruling allows that the materials themselves have a "stored potential" then perhaps there is an option to say it might work. e.g. The character who walks between the worlds is carrying a powerful gryphon claw into 1920s New York setting. The claw is inherently otherworldly, but so too is the character. The game has allowed an alchemist to get there, so why not the claw? Tricky.
I thought from previous editions of the GURPS rules that zero mana worlds did not allow magical items (and therefore alchemy too) to function as they were required to draw ambient mana from the world around them. The laws of physics do not allow for mana, so it is non-functional, as is everything which depends on it.
I'd argue in a no-mana world the ingredients are just "plain" materials. They do not perform any quasi-magical function because it is in contraction to the World setting. This is a significant disadvantage to the alchemist/magician player character, so I'd question that character's role in the no-magic setting.
In a low-mana setting (which is in the description, but different to the question title) the alchemy would work, with a proportionally reduced effect. The world lacks the normal magical energy to make the ingredients react in the proper "high magic" way. Like trying to boil water when sufficient heat is not present.
