Yes, they do.
They may not think the functions are going to be eliminated, or most of the rank and file staff removed from government service, any more than when the predecessors of various parts of ICE, like the INS, were abolished before it.
You're right about Occasio-Cortez: she is shaping up to be about as bad as Trump in this respect. I'm not quite sure which of them is worse, but I know the prospect of her someday getting to the White House is a chilling prospect, even though my political leanings are in that direction. She appears to be about as dangerously ignorant (and perhaps callous) of facts of situations. The only mitigating factor for her is that perhaps experience will temper this, and maybe she is just uninformed but not unwilling to learn.
Citation needed.
AOC is not eligible to run for president until she is 35. These facts might calm your fears.
It's like when Dems say they want to abolish ICE. That's what their base want to hear. Do they really think ICE is going to be abolished? No, do they like hearing that because it rings nicely in their ears. yes!
Let's abolish ICE is the lefts version of "Mexico will pay for the wall". When they say Abolish ICE, they mean we'll (try to) do the dreamer things and we'll be less literal on refugee interpretation (and include economic migrants as definition of a refugee) for example. And, if it doesn't happen (not enough internal support) we'll blame the Repubs, no loss on their side. This is how political comms works.
Don't try and hang them on each and every word. You'll miss what they are saying.