Does Smoke Screen make a unit might go 0?

No, Smoke Screen does not make a unit's Might go to 0.

According to the card text and the established rulings for Smoke Screen, it reduces a unit's Might by 4, but it includes a minimum of 1 Might restriction.

As detailed in the FAQs:

• Smoke Screen's limitation: The "cannot be reduced below 1" text limits the magnitude of the reduction at the time the spell resolves.
• Snapshotting: When Smoke Screen resolves, it calculates the reduction amount based on the unit's current Might (including active passive bonuses) and "snapshots" that reduction value for the rest of the turn.
• Future changes: While Smoke Screen prevents the unit from being reduced below 1 Might at the moment of resolution, other effects that occur after Smoke Screen has resolved can still reduce a unit's Might below 1 (to 0 or even negative values).

In summary: Smoke Screen itself will not set a unit to 0 Might, but it does not prevent the unit from reaching 0 Might due to subsequent effects.