Wouldn't recommend it unless you were to maybe screw it on using slotted holes. Depends on the size as well.
If it were me I would add end grain strips to the the side of it. Just means a little more work.
Id also be careful of gluing the board if it has any finish applied to it. Depends on the finish but for my boards I soak them in mineral oil. I wouldn't try to glue to that unless its had a chance to dry out for a good few months, Even then it might be hit and miss as mineral oil doesn't dry.
If its a drying finish a good sand will take that off ready for gluing.