Can it be done? I feel like you have to be standing up to impart the proper action. 

I have, but its definitely far easier to do it standing. I ended up using a side motion.

You read my mind this morning -- I have almost no experience with jerkbaits but was trying to fish one from a sitting position in the kayak earlier today and friday morning. The best I could manage was a shortened side motion as mentioned above, similar but harder (and less rhythmic) than what I do for walking a spook.

Yes, you can do it but you have to use a sideways motion and it does work, just not was well as the proper straight down technique. I watch a friend use a 7' 1" rod and he catches fish with the sideways rip, not as many as I do but it does work.

I've done it. Like stated above it takes a bit of creative technique to impart the desired action, but it can be done. 

I have a pontoon boat and use a jerkbait all the time. I must of hooked 10+ smallies this morning on a Shadow Rap. I use a side and down presentation from a twitch to a rip.

I fish both soft and hard jerkbaits from a kayak and have no problem.  Same for walking frogs too fwiw.  I don't see the problem.  

It is harder but it does work

I do it all the time and found that its easier with a spinning rod vs a casting rod...at least for me.

Jerk baits are better fished standing up Kayak or no

Think about it this way.  In a kayak you are already low to the water and your rod tip is where you would be if standing in a conventional boat.  In essence your rod tip is in the same position and essentially doing the same motion.  Whether you are moving your rod tip down or to the side, the bait doesn't know the difference, it is just the line being pulled.  Position your kayak so that the line is pulling the direction you want and it will be all good.  

The other option is buy a kayak you can stand up in if it is that much of a concern.  

frankly i don't think it's any more difficult than trying to do a "walk the dog" type motion from the kayak.  definitely doable and made way easier if you can stand and fish from your yak.