I suppose the question is not correct. HDR is possible using e-shutter. My cameras, specially the GX85 which is sticking on e-shutter, does it without problem.
The real question, I guess, is that HDR will usually use 3 or more burst shots to merge into a HDR output (if I get you right you were actually talking about in-camera HDR?). If there would be movement within the frame, it could result motion blur on the HDR output. E or M-shutter would be the same.
When I do exposure bracketing, e.g. 7 shots of 1 stop per shot, sometimes if there would be a pedestrian walking from acsidecto another, he might appear in different position of each frame. For some HDR software, I could get an output showing along tail of that person. For some smarter HDR software, I might get an output of minimal to no motion blur.
Any sort of stacking would have their limitation on application. Some scene are good for HDR and some not.
Not sure how phone works on this. Generally I am not happy with phone's IQ. YMMV.