Not sure if you mean the relics that are in the cavity/sepulchrum of an altar or relics that are in a reliquary which is placed on the gradine of the altar?
Most altars have a sepulchrum, so yes, the priest would pray the Oramus te, domine.
If there wasn’t a sepulchrum, then I would think not, but not being a priest I couldn’t tell you for certain.
Perhaps @edward_george1 will be able to advise you on this.