Historically speaking, groups that are given everything they demand don't dissolve; they ask for more stuff. This is regardless of the "goodness" or "badness" of the demands.
Well, if you negotiate them stopping and they are centralized enough to respond to a negotiated agreement you can give in to some demands and that'll be that. Sometimes this works (the ends of most wars between nation states, the British agreement with the IRA), sometimes the other side decides to screw you over (see the vikings vs England, Hitler), and sometimes the other side isn't centralized enough that negotiating even makes sense (Al Qaeda).
So there are times when it works and times when it doesn't, but we can be pretty sure it won't work here.
Sometimes more than others. The civil rights movement largely dissolved after achieving most of its demands, for example. Many of the individual participants continued to campaign for additional causes, but the movement didn't continue with anything near its prior strength once the Civil Rights Act and Voting Rights Act were passed, because they couldn't hold together the broad coalition around a new series of demands.
I have to take issue with this statement. It didn't just "dissolve" bad things happened (what happened the Martin King and Malcolm X is well known but also look into the fate of the Black Panthers) to all of the leaders and the movement floundered without its stronger figure heads.
That's what is so vitally important about the amorphous collective form of Anonymous and even later Occupy Wall Street. Without a clear head to cut off or discredit the movement can continue with its goals even if it loses a few people.
I think that's part of it, but I do think satisfying some of the major demands dissolved the broad coalition; moderate liberals, especially white liberals, were largely satisfied by the civil-rights legislation, and dropped out of the movement, leaving a much smaller activist core. The SNCC took a huge nosedive in membership after 1965, for example, and even MLK found it harder to muster the same levels of support for his post-'65 causes (like desegregating Chicago, and ending poverty).
I guess you could look at some unions as an example. They ask for things to the point where in some places people can't use a broom to sweep up their workspace because that's a 'union job' and it would take away a job from a union member.
So there are times when it works and times when it doesn't, but we can be pretty sure it won't work here.