The simple answer is yes. My parents have a grape trained over their pergola:-)

Just remember to never prune it in spring as they can bleed sap and die. Always prune in mid winter any laterals back to a few buds once the permanent framework of branches has grown into place.

Many thanks. Could you tell me if I just use the longest stems to form the frame work on the cross beams of the pergola? Is it safe to cut back any laterals growing on the vertical structure?

Longest and strongest are probably best. It might take a couple of seasons so don't try and drag stems across or take short cuts. Let the plant grow into position itself and select the best stems to become the permanent ones.

You can prune in summer and remove any laterals if needed as long as there is plenty of growth higher up.

Many thanks