Yes, and most people underestimate how much. The cutting board is in contact with the edge every time you use the knife, and the material it is made from has a direct effect on how quickly that edge degrades.
The worst offenders
Glass and ceramic boards are genuinely damaging. They are harder than the steel of the blade, so every cut is slightly abrading the edge. The edge rolls and chips faster than it would on any reasonable alternative. There is no good reason to use a glass cutting board with a good knife. They exist, I assume, because they look clean and are easy to wash. The cost is paid by the edge.
Stone boards and marble surfaces are in the same category. Beautiful in a kitchen. Destructive to edges.
Plastic boards
Plastic is softer than steel, so it does not abrade the edge the way glass does. But it is also less forgiving than wood — it does not have any give. The edge contacts a hard, flat surface every cut. Regardless, they leave tiny pieces of plastic behind in your food. Therefore I strongly advise against plastic cutting boards.
Wood boards
End-grain wood is the best surface for a good knife. The edge enters between the wood fibres rather than across them, which means the wood gives slightly and the edge is not pressing against a hard flat surface. Edge life is noticeably better. The board also self-heals to some extent — the fibres close back up after cutting.
Face-grain and edge-grain boards are fine too, and more common. They are harder than end-grain but much better than plastic or glass. Hardness of the wood matters — a very hard wood (teak, for instance) is tougher on edges than a softer hardwood like walnut or cherry.
Additionally wooden boards are a lot cleaner than plastic boards, as most woods have an natural anti-bacterial effect.
The practical takeaway
If you have a good knife, use a wood board. End-grain if possible, any good hardwood otherwise. Avoid plastic, glass and ceramic entirely.
A knife that lives on a wood board will stay sharper longer and need less maintenance. It is one of those things that costs nothing to get right.
More on keeping your knife in good shape in my knife care guide.