We often answer questions such as "What are the primary differences between camera a and camera b?" in terms of how those differences affect what types of photographs those specifications make possible or make impossible. Many times one of the features considered important to some types of photography are things such as frame rate and buffer depth because they affect what it is possible to photograph with that specific camera. Likewise, we sometimes answer the same question in terms of dedicated controls on the camera body that allow faster handling and changing settings in challenging shooting conditions in order to catch moments in rapidly changing conditions.
If I'm shooting a sport and want to catch a sequence of something that requires 8 fps to capture each distinct step in the series, then I need a camera that can shoot at least 8 fps under the conditions in which I am shooting. A camera that can only shoot at 5 fps will not allow me to get the shots I want/need. The same is true if I take an 8 fps camera and cripple it with a slow memory card that artificially limits the maximum frame rate and buffer depth of the camera.
The speed of a memory card interface has a direct bearing on the burst rate and buffer depth of digital cameras. I can take an older, slower card and put it in my Canon 7D and the number of consecutive frames I can take in burst mode before it slows to a crawl is halved from a card that runs as fast as the camera is capable of writing to it. So yes, the performance of the memory card, which might include that architecture of the interface, can have an effect on the photographic possibilities.
Although we often say and hear that "gear doesn't matter", the truth is it doesn't really matter until it does. And then it really matters. When the gear limits the capability of what the photographer can accomplish it matters a great deal.