This is a tough one! The reason I say that is.....I started my photography career working with equipment I could afford (just like most photographers), which was not thought of as 'the best' make or most professional equipment. Like many people working for themselves, unless you are lucky enough to have a large investor, you make good with what you have!
I openly admit that the first few professional jobs I did, meaning I was charging for my time and an end product, were a steep learning curve, both creatively as well as technically. I had always believed that the big named brands in photography equipment were just that, big names and that the other smaller brands could compete. Technically, due to the fact that I was working successfully and charging for images taken with a 'lesser brand' camera, I was right.
As I have had further work requested and been commissioned for other work, I have to say that I was wrong in thinking that the name brands are nothing but a name. To a point you will always find 'less useful' pieces of equipment, that many think are vital just because there is a brand name on it. I've made those purchases!! :-)
As far as weddings go - equipment really is important, as far as quality.....not quantity. Does it matter to the bride and groom that you have 10 Canon L lenses or Zeiss lenses? No. Does it matter to the bride and groom that you have the right lenses? YES!! If you use 1 lens to capture a whole wedding but use it properly and know it's ability and because of that can crate the images that fit your style and create images that are equal to what the bride and groom booked you for then that's great and you could say that your chosen lens is very important but the amount certainly isn't! If you feel you NEED 10 lenses to capture the wedding in your chosen style, that's great too and to that photographer I would presume that the quantity of lenses is also very important - but it carries absolutely no interest with most couples.
I have proven the fact that it doesn't matter time and time again. I have shot a paying wedding on an old Olympus E510 which is at best a lower-mid level enthusiast camera. Did I feel wrong doing it and charging for my service and products? No, because I understood it's limits and capabilities and was able to create my chosen style with that camera and the Zuiko lenses I was using with my surroundings.
I do have a preferred brand that I use and currently that is Canon, does that matter to most couples? No! I don't spend thousands of pounds on equipment to impress anybody, however I do spend thousands of pounds on equipment to provide consistent, high quality imagery and a high standard of image reproduction. That being said - I am a firm believer that the image at the end is only ever as good as the photographer at the beginning!
To be honest, this question is an impossible one to answer. To me my equipment quality of the chosen pieces of equipment and back-up equipment I have is extremely important. To another photographer it may be the fact that the camera is small and light, because it fits his/her style. Their doesn't seem to be a wrong answer.
Does Equipment Matter? Hmmmmmmmmm That's a tough one!! :-)