I'm working on something very similar right now, so it's great to see that this is actually possible with currently available open-source resources. I'm trying to re-create Skype's background blur feature, but that I can use in OBS (obsproject.com) so I can apply it just to my webcam without messing up the other stream elements for online lectures.
I've been using the the DeepLab model from tensorflow research repo to do segmentation, but BodyPix seems even better for the job. If it performs any better, this might be the break I was looking for...