OP isn't devoid of logic. Volunteering is kind of like saying you think your chances are better elsewhere. Could Intel resent that? Sure. Even though they need to cut heads, Intel might not look at the volunteers positively.
But I agree with Reply 1 that anyone that they retain means they really NEED that person. Intel won't be thrilled that person was ready to jump. It's just that Intel NEEDS that person, RIGHT now. But who knows, as soon as they have a plan B, maybe they will get rid of the volunteer.
As far as not fearing future rounds - the problem is that in the future might not be as good a time to leave. Say you're young, married, no kids. You throw your name in the hat. Rejected, Intel NEEDS you. Now, two years later, you've got a kid, or maybe two. Down to one income, and you need that income. So it might not be a great time then.
So, I see both sides.
I'd say, if you are in a good place financially and like the package (or think things are only going to get worse), then take it, and don't worry about the management fallout.
If you're happy, stay.
There might be some fallout from volunteering, but from what I can tell, management will take nearly every volunteer.
YMMV. Good luck.