Does Green-Flame Blade get Alchemical Savant bonus if you use Alchemist Supplies as improvised weapon?

The Alchemist’s Alchemical Savant ability states

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 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 it benefit from Alchemical Savant?