If an object with some mass was sitting there floating in space then suddenly lost a little bit of mass, would this cause an acceleration of the object?

Depends on a few things.

Normally this would be an F=ma problem, but we don’t know enough about the starting conditions.

Scenario 1. The mass was at rest or was at a constant velocity with no acceleration, but loses mass without additional force. The mass stays at rest, or no acceleration.

Scenario 2. The mass was accelerating, but loses mass without additional force. The mass increases its acceleration.

Now if the change in mass results in a force things get more difficult, but I think we covered what you were really asking already.