I know what a false dilemma is. I'm not sure you do, though.It becomes a false choice. Free-will is greatly reduced if the Abrahamic God is obvious and overt?
False dilemma - Wikipedia
Yes, they do have a choice.Example: A Homeless person is dying of hunger. They walk passed a 20 dollar bill on the ground. No one is watching. Do they really have a choice whether or not to pick it up? No, it's a false choice.
The question of which choice is best may be obvious, but that doesn't mean that the person didn't make a decision to pick up the money.
... but just to play Devil's Advocate: let's go with your (IMO wonky) approach to free will. By that standard, our free will is violated all the time... so why would you assume that God is interested in preserving free will?
No, there still is a choice. A choice where one option is the obvious choice is still a choice.It's the same if the Abrahamic God is proven to exist and that the blessings and curses are real if each person chooses to obey. There really isn't choice at that point. The blessings are too tempting, and the curses are too painful. As soon as those become real and obvious for everyone, there is no choice.
"No choice" would be a scenario where, say, someone managed to control your body remotely and made you do something without you deciding to do it.