During the initial casting it's a levelled spell so I believe he can't at first, but after the spell takes effect you can use the attack without expending a spell slot does that make it count as a cantrip for the purpose of multi-attack?
No, on two counts
Per the spell description:
The touch of your shadow-wreathed hand can siphon life force from others to heal your wounds. Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt. Until the spell ends, you can make the attack again on each of your turns as an action.
Nothing in the rules changes a leveled spell "into a cantrip". They are two different things and just because a spell is on going, does not change its level. The character must concentrate on the spell at the level at which it was cast.
Even if it became a cantrip (It doesn't-see point #1), to use the spell on successive rounds, you need to use it as an action. It takes up your whole action so multi-attack does not even come into play. Your Action is continuing the spell, not the "Attack" Action.