Just another interested customer here. The way it looks is the QC can do two things. 1) run full models of specific amps, effects, etc. (like any plugin, modeler, Axe Fx, etc.), and 2) capture any part of a signal chain or the entire signal chain in a static sense (like a Kemper).
#1 is fairly explanatory given all of the existing options that have been on the market for a long time. All of the knobs and switches of the physical device that is being modeled should be present in the QC in theory and the functioning should be comparable to how the physical device actually works.
#2 the ability to have both amp captures/profiles and amp models in the same box is something that has not really been done yet, and hopefully the QC will be a top dog at both. But to answer your question, it appears like these captures can only be static; it is just a function of technology. The unknown is how much the QC might allow you to modify a capture after it is done. The Kemper lets you tweak a profile some after the fact, the available controls are not like turning a knob on the real amp, but it sill gets its many users where they want to go.
One of the biggest things that seems like it will set the QC apart is the ability to run multiple captures in a single preset and scene. This implies you can theoretically put a capture of a drive pedal at the beginning of your chain, a capture of the preamp section of your favorite amp next, then a capture of the power amp section from a different amp, all without having to have all of these units hooked up in reality to capture this complicated signal chain into one combined static capture (unless you wanted to). The question for me is will the QC’s capture magic actually do a great job at running one capture into the other and still netting very similar results in tone and feel as if you actually captured the same combined signal chain in reality. It seems like a tough ask, but it could put it even further into unicorn status if it does.