It does indeed make a bigger difference there, but even while climbing it shouldn't.
The reason it does is because most people's climbing technique isn't good enough not to.
Think of it this way:
If you would have a rigid fork ... let's say an aluminum or carbon fork ... and you would pedal uphill the way you do ... that same technique that makes the suspension fork compress while you do it.
Where would that (excessive) downward energy go?
It certainly won't simply not be there anymore, right?
Would it go into propulsion? Probably more than with a suspension fork, but a lot of that energy will simply squish your front tire and will be lost on hysteresis there and decreased rolling efficiency.
You don't want that.
Try to ride your loose suspension fork uphill ... while keeping the fork as stable as possible.
It will seem difficult at first but after a while you'll manage and there you have it: pedaling efficiency resulting in more propulsion and less wasted energy.

The trick is to pedal in circles and at a high cadence.
Pulling up slightly on the upstroke, actively moving forward on the top, pushing down but not too much on the down stroke and pulling back like you're scraping your foot on the bottom.
All of this at 90+RPM.