I've never been able to feel tampons when I pushed them all the way up. At least not feel in a way different from diffuse pressure that I'm not sure whether it comes from the tampos or the period.
The problem I have with tampos is that they tend to get close to the entrance when I pee, so I have to change them a lot. Of course I have missed most of my periods for the last half year or so (hormone issues), which is bad, because: hormone issues, but I can't really say that I miss the bleeding part, even though the only other symptom I usually get is having to pee a lot.