Depending on the genre of comic, I would say readers definitely do care about the storytelling skills.
Just think of it in the reverse. There have been plenty of official works with strong starts, but their stories regress overtime and people complain when later seasons/chapters/arcs aren't as good as the beginning. People do notice these things.
Likewise, something with a weak beginning can get better along the way. I've had old readers go back to my earlier episodes or other uploads of my comic and leave a comment telling new readers that it's worth the ride. Unless you intend to change a story's plot or premise entirely, I would usually suggest continuing your comic instead of starting over.