Likely, as I know that during a time crunch (a few old people died the same day) a priest had to change a Daily Mass to a funeral Mass in order to get them all in before Ash Wednesday. He let us know and he allowed the group that was doing a novena to stay afterwards and pray, where, normally after a funeral he’d close the church.
However, I think that it would depend on the stipulations of whatever indulgence you are trying to obtain.
