Short answer, no. long answer, not usually.
The caveat is whether the focus on the rear shoulder unmindfully results in you slipping back into the habit of starting the putter away from the ball with a tug of the hands and forearms instead of a shove back with the lead shoulder. the handsy start has a high potential for creating a backstroke problem of some significant difficulty -- taking the putter back outward across the line of the putt, creating a loop coming forward.
All of this "focus" stuff is not necessarily incompatible with USING the better or best pattern of muscle activation for a good, reasonably trouble-free backstroke. So you can have your "focus" cake and eat your "good muscle pattern recruitment" too. focus on the right shoulder going up, but use the left shoulder's getting moved down by the mid-torso muscles to make the right shoulder move up.
You don't really have a choice about that, actually, because the muscles that move the right shoulder UP are the SAME muscles that move the left shoulder down by tugging the left side of the rib cage down towards the left pelvis. There are no muscles that LIFT the right shoulder frame on the right side. (I'm not talking about "hunching" the right shoulder by itself: just moving the whole shoulder frame.)
Your focus on the rear shoulder in this case ought to be a little more specific than perhaps you realize. The focus is not simply on moving the right shoulder UP, but on moving it straight up from the surface, so that the right shoulder does not drift to the rear of the original shoulder alignment at address (i.e., right shoulder should not go back horizontally).
The above is all IF you are trying to eliminate arcing inside on the backstroke. The bottom line on WHETHER you should worry about the backstroke path is: no, not if you can resquare the putter face and reset the shoulder frame parallel to the target line no later than when the putter head returns to the bottom or middle of the stroke, so thereafter going forward the putter face stays square and stays moving straight online thru impact and a little past the ending of contact between putter face and back of ball (2-3 inches in front of the back of the ball is plenty for this impact zone.)
Can this be done and if so HOW? Sure, just anchor the left hip in place before starting the backstroke. Then any turing horizontally back of the shoulder frame (and right shoulder) "closed" with respect to the line of the putt or aiming across the line to the outside of the target is as if attached by rubber bands or a bread-crumb trail of abdominal muscle and tissue back thru the dark forest to the little cottage "home" of the stationary left hip. Then when the forward stroke commences, the inner muscles and other tissues "stretched" away from "home" will effortlessly guide the torso back to square like a spring-hinged door closing on its hinges into its door frame. (This is a Seve Ballesteros bit of lore.) Don't allow this closing to continue past square, though: stay square once you return to square or else you get a pull stroke.
This all seems to mean: if you like straight-back for the backstroke, focus on the rear shoulder is okay and probably won't hurt so long as you remember what moves the shoulder frame and USE that pattern, but you don't need to get perfectionist about it -- reduce the arcing and be happy and forget that, without belaboring getting perfectly straight back. Just anchor the lead hip and then do your thing with focus on tempo and how pleased you are about not having to worry about the stroke!
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