This device would be useful to my FIL, he is 86 and still cuts his fire lumber with an axe or with a chain saw, at his age he gets tired of lifting the chainsaw and moving it up and down to cut the logs, so I think that a branch is lighter to move than the chainsaw, and it gets lighter and lighter with each cut.
To improve safety I would make the chain run between two pieces of sheet metal to avoid accidental contact, those two pieces would have an lightly inclined notch big enough to accomodate the biggest branches that one would cut, and in between the pieces occupying part of the notch I would place the accelerator lever so that when placing a branche on the notch it would accelerae and the branch would be pressed against the notch by the advancing chain.