Dear Hugh,
No.
In fact, Dave Pelz in his video Developing Great Touch makes a clownish point of putting with large mits, to show that "touch" in the sense of distance control does not involve feeling in the fingers or hands. I agree with this general point, although I disagree with pelz about how touch actually works in the brain and body.
To address that -- touch relies upon tempo and targeting for the most part, and the resulting body movement is planned non-consciously, which is what most people label "instinct." Even so, the movement during the stroke has some feedback (visual, kinetics, and haptic of "feeling" by sense of touch). The feedback most people talk about is feedback AFTER impact -- vibrations in the shaft and handle from the putter-ball collision, and a sound. The more important feedback is that received DURING the stroke. The purpose of this feedback is to make sure the Tempo-Targeting system is being allowed to work properly -- that is, without interference by your conscious and well-meaning but misguided thinking and trying instead of using your instincts. The way this feedback helps that process is to make sure you're not moving the putter otherwise than inside the smooth tempo.
If you start the putter back too quickly or abruptly, the forces of the putter make it "lever" inside your grip and you can "feel" this. If you stop the backstroke too quickly, the hands "feel" this also. If you start the putter down too abruptly or torque the putter in the downstroke or twist the putterface with wrist or finger activity, you can "feel" this. If you tighten the grip in anticipation of impact, you can "feel" this. If the wrists or hands or forearms become involved in guiding the putter, you can "feel" this. All of these instances of "feel" are bad. In the ideal stroke, you will not feel any of this. So the feedback you want is "NOTHING HAPPENING" in the hands.
Back to the gloves -- a golfer CAN make a good stroke without after-the-fact "feel" of the impact, which is Pelz's point, but Pelz does not teach the feedback DURING the stroke. For this, you do need the sensitivity of the hands to monitor the stroke for tempo and regularity. Even so, one golf glove on the left hand of a right hand golfer does not really prevent this sort of feedback. By the way, the left hand is the only hand in FULL palmar contact with the putter, so it is the more important for monitoring the stroke.
Cheers!
Geoff Mangum
The PuttingZone
http://puttingzone.com
Golf's most advanced putting instruction.