If you can change the damage type and if you are using the RAW ruling for magic missile, I would say yes. But there is no way I am using the RAW ruling for magic missile in my games.
Unfortunately, magic missile and alchemical savant are star-crossed. There seems to be a synergy there, but never the twain shall meet.
You could get access to and change the damage type of magic missile to, say, fire, by taking 2 levels of scribes wizard. However, magic missile would not count as an artificer spell for you, and so you cannot use your alchemist’s supplies as a spellcasting focus for magic missile, and so you cannot apply the bonus damage from alchemical savant. No, I don’t buy the argument that because alchemist’s supplies contain a stirring rod, and a wizard can use a ‘rod’ as spellcasting focus, you can get around this. That argument is essentially saying that a stirring rod is equivalent to both ‘alchemist’s supplies’ and the ‘rod’ that is mentioned as among the wizard spellcasting foci options, which is clearly untrue.
You could try to get around this by taking the artificer initiate feat, which allows you to choose a tool proficiency (e.g. alchemist’s supplies) and then thereafter allows you to use that tool as a spellcasting focus for any spell that uses intelligence. Casting magic missile as a scribes wizard still uses intelligence, so with the artificer initiate feat couldn’t we use our alchemist’s supplies as the spellcasting focus for magic missile, and thus benefit from alchemical savant? Unfortunately, I still don’t think it works RAW, because magic missile does not have a material component at all. In order to use a spellcasting focus, a spell needs to have a material component. All Artificer spells count as having a material component, yes, but magic missile is not an artificer spell for an Alchemist. The artificer initiate feat allows us to use alchemist’s supplies as a spellcasting focus for any spell using intelligence, but that doesn’t mean that a spell that didn’t have a material component suddenly has one. That’s true of artificer spells, but we got magic missile through being a scribes wizard, so it’s still a wizard spell.