It ultimately depends on how pristine you want to keep it vs how particular you are when it comes to doing things the “right” way.
Can you use a jack with rough exposed metal? Sure, but it’ll scrape up the contact area.
Can you use any rubbery/soft flat pad? Sure, no problem.
Do you need a pad with the nipple to slot into those point? Nope, it just makes aligning the jack a little easier. Put the pad it first and then you’ll know where to line up the jack.
But if you’re a person that pays attention and doesn’t just haphazardly does things, as long as the jack has a non-marring contact surface, it’s fine.
edit:
I just checked the link... I bought those pucks! I did it cause it definitely is easier to line up the jack... plus, I'm missing the rubber inserts on my jacks. I know two of them got sliced in half by the pinch weld of the Honda HR-V I had. Apparently it was just so heavy that the weight cause the 1/4" (or 1/2"?) pinch weld bend to still act like a knife and shear through the rubber.
One problem I just remembered. I don't have enough clearance to use the pucks (sat on the jack or inserted first) with my 3 ton floor jack. So I have to use my smaller, 2-1/2 ton floor jack. Maybe I'll look around for another puck that's thin enough.