For my no-death runs I count it as a death. If I recall correctly, the edges of the screen go red and the death scream is triggered. My memory could just be bad, though, and if it is, then I would still count it as a death anyway. Functionally, it is no different from Lilith using Phasewalk to run off of the cliff around Crawmerax. She will respawn downstairs without paying the death fee. Another version of that is avoiding death by turret in Rust Commons West when getting the red chest that is out of bounds. You can walk off the cliff in a specific way to avoid the fee, but it is still a death as far as I am concerned. Also, saving and quitting to avoid death is something I regard as cheating.
The only absolutely unavoidable case of getting to Fast Travel without a fee is doing the Armory missions. Besides being forced by plot, the only excuse for this one is a lack of both a death scream and the screen going red. It would have been nice if you could just plant the bomb, then leave, but such is life. It could have been cool to get a “walking away from the big explosion” cinematic for it.
Back on topic, it is ultimately up to the rules you set for yourself. I have plenty of self-imposed rules, such as no entering the DLCs out of order, or after the completion of the main plot. You could just as well treat it as a giant safety net for the area if there is no red screen/death scream if your conscious is okay with that.
Everyone has different rules. I used to fight Mad Mel in a way fellow no-death player MeltintheSun (if I recall his name correctly) regards as cheating (parking vehicle on ramp, running inside to trigger fight, running back and jumping in the vehicle, jumping out and relatively safely sniping Mad Mel while only taking damage from the occasional rocket or thrown buzzaxe) for his purposes. I now use a new way that could also be regarded as cheating (I jump up on a rock inside the arena, and for whatever reason I cannot be hit there) as it is even safer than the old way. Are they both cheating? One? The other? Does it matter? Let your conscious decide.