Historically yes, and even more so with modern systems which optimize around modern best practices. For example, Unreal Engine's Nanite breaks geometry into hierarchical clusters of triangles.
If the triangles are long and thin, they end up stretching across the screen and mess up Nanite's hierarchical streaming and culling system.
Shading artifacts also crop up on long, thin polys.
Dense geometry with hierarchical streaming will perform better on large datasets than sparse geometry with long thin triangles and traditional approaches.
Mobile GPUs use tile-based rendering. A long thin triangle touches more tiles, so it costs more. That could make you think you need to use Delaunay all the time. But the gain from nicer Delaunay triangles on the GPU is small relative to the time you pay for Delaunay on the CPU. I've measured time profiles on map data. It could be that for games it pays off.
Definitely, you have to understand where your bottlenecks are. That's why it's best just to author good models.
Nanite/triangulation can help relieve GPU bottlenecks but if you're already stomping your CPU it won't help. Whether it's a good fit depends on your workload.
If the triangles are long and thin, they end up stretching across the screen and mess up Nanite's hierarchical streaming and culling system.
Shading artifacts also crop up on long, thin polys.
Dense geometry with hierarchical streaming will perform better on large datasets than sparse geometry with long thin triangles and traditional approaches.