The pop is much more noticeable with the DCO oscillator, although I don't have to dial back the Attack as much to eliminate the pops for that OSC as I do with the VCO one.
EXAMPLES:
I designed a super-simple example patch to illustrate the problem. It's a single-oscillator sine wave intended for use as a sub-bass modifier for a kick drum. I ended up having to ditch Element for another synth since I couldn't get rid of the pop without losing too much of the attack.
Here's a screenshot of the "zero attack, DCO OSC" variant. (Note, I uploaded all patches mentioned in this post to this directory.)

EDIT: KVR's in-browser audio preview thing isn't working for me. If you can't hear these clips, you can play them directly from here.
And here's how it sounds: sub_kick_dco_no_attack.wav
Here's the VCO version of the same patch. Still definitely a pop, but not as distinct: sub_kick_vco_no_attack.wav
In order to get rid of the pops on the DCO version, I had to increase Attack to 17ms: sub_kick_dco_17ms_attack.wav
And to do the same on VCO, I had to increase attack to 27ms. Completely unsuitable for my needs. sub_kick_vco_27ms_attack.wav
All the original patches and WAV files are available for download here.
Here's a zoomed-in Audacity screenshot of one of the zero-attack DCO pops:

QUESTIONS: Does anyone else experience this with Element? Is there a way to fix it?
