What I feel like about this is that it is possible, but it would be unintentional.
It's easy to slip tongue and not pronounce 요 clearly enough while speaking fast. Especially, 했어요 sounds very much like 했어여 sometimes. (Yeah, I admit it.. it's me.)
However, ordinary native speakers wouldn't consider themselves pronouncing ~요 like ~여 at the end of sentences.
The youtube linke you provided spells everything with -여, instead of -요, but I find it very strange from a native speaker's perspective. (I live in Seoul) Like I said above, native speakers would still consider themselves that they are pronouncing -요, not -여 at the end of the sentence.
However, I admit that the pronunciation of -요 has become vague compared to that in the past. So, it might be that the dialect is actually in the process of changing. The reason I'm saying this is because I've watched a youtube with Seoul dialect in 1990s, and I felt they articulated each syllables much stronger. (Guess what? I was in Seoul back then as well, and I never thought the pronunciation has changed a bit.)