The Alchemist artificer's 5th-level Alchemical Savant feature states (WGtE, p. 180; E:RftLW, p. 58):
Whenever you cast a spell using your alchemist’s supplies as the spellcasting focus, you gain a bonus to one roll of the spell. That roll must restore hit points or be a damage roll that deals acid, fire, necrotic, or poison damage, and the bonus equals your Intelligence modifier (minimum of +1).
Green-flame blade (SCAG, p. 143) is not on the Alchemist's spell list, but it lists "a weapon" as the material component for the spell. This is presumably the weapon used in the attack.
If an Alchemist casts green-flame blade using their alchemical tools (e.g., a beaker) as an improvised weapon attack, would the fire damage benefit from Alchemical Savant?