I think you're definitely engaged, but not so much with the moment itself more with the act of taking photos. It does make you focus on the subject, but in a very specific way. Even in how you described it, the main focus was on capturing the shot. It quite literally makes you look at things through a certain "lens".

You can see how that might be a bit of a problem when you're sharing the moment with others. You might end up being really focused on getting the photo and not as much on actually being present with them.