Edit: Doh. Misread your question as about trouble aspect, rather than consequences.
Still, I'd agree: yes, you can invoke consequences, though doing so should (as others have mentioned) be a bit more difficult than normal. For an example of this in the rules, consider the death curse, where you explicitly get a free tag off of any consequence you've already suffered.
Oh, absolutely. It's an aspect like any other; if you can get some advantage from it, go for it. Of course, any time you do invoke it, should be a cue to your GM that it should also be complicating things...
For example, a character with a "hero complex" might invoke that to help fight a denarian... but could then be compelled to let the villain go when it pulls a standard "Do you want to finish me... or save those innocent civilians that are about to be crushed by a collapsing building?"
Or a character whose trouble aspect is "curiosity" might invoke that to get more information out of an investigation or contacts roll... but could then be compelled to go just a bit too far and, say, tip off the villains that someone was looking into things.
As I see it, the main purpose of the trouble aspect is for the player to tell the GM: this is the big thing I want to have causing problems for my character. And it accomplishes *that* just by being written down; no need to limit its use as an aspect.