"Can you open a 'Gravity knife' when in a free fall during a parachute jump? Has anyone tried it?

Now I mean open it like it was intended, by sheer gravity and not by flinging it out with a snap."

Theoretically, no.  Provided the knife is perfectly inverted during your descent, he handle from which the blade usually falls would be falling (& accelerating) at the same rate as the blade (& the user).  In practice, things would likely be jostling & bumping around, & the knife angle would likely change, allowing the blade to either slide out or be forced back into the handle due forces other than gravity acting on it.

So, if someone tells you they tried this exact stunt & the blade came out, they're either messing with you, or those other forces (& NOT gravity) caused the blade to come out of the gravity knife.  

This is an instance in which anecdotal evidence will likely have incredibly limited value to the answer of the basic (theoretical) question.  As with most anecdotal evidence, too few variable are accounted for when coming to the conclusion.  

And don't believe anyone that tells you the blade will come out because it's heavier than the handle, that's just not how gravity works.

The army currently requires the knife to be secured by thre securing devices when you jump. I don't know how strictly that's enforced. The US Army normally had pocket switch blades Along with a fixed blade in WWII I'd suggest something other than a gravity knife if you're going to need it cut a fiwked chute

The army currently requires the knife to be secured by thre securing devices when you jump. I don't know how strictly that's enforced. The US Army normally had pocket switch blades Along with a fixed blade in WWII I'd suggest something other than a gravity knife if you're going to need it cut a fouled chute.

Heck when were training. They'd even make up tape our fixed blades into the sheath just for a helicopter ride!