No - the demons do not assent, trust nor are open to God even though they know He exists.
Maybe this can help:
Faith
Thank you for that link. It describes
FAITH!!! very well.
I would like to add that many people have
FAITH!!!. Some Catholics have

:angel1::harp::bible1:
FAITH!!!

:heaven::grouphug:
Leela, if you can’t understand why I made the word “faith” larger, used all upper-case letters, bolded it, underlined it (and the following exclamation points), changed the color of the letters, and added religious symbols, I will explain. It is difficult to use the computer as a means of communication. You can’t see my body language or hear the inflections in my speech and I have the same problem in reference to yourself.
So I have to rely on other means to communicate my meaning. I think it is clear what I mean - those who have faith in God and the Catholic Church as the Church founded by Jesus, one, holy, catholic, and apostolic, as the Bride of Christ, against which the gates of hell cannot prevail, is faith in Truth. The Catholic Faith is the only true faith. It makes no difference if others don’t see this - Truth remains Truth. Truth is. Catholics are blessed to know this. We know our faith is a gift sent to us from God in love.
If I could have I would have used a cursive font and have had more angels and crosses and other symbols and beautiful music playing whenever you look at the huge “faith.” But I’m pretty much computer illiterate and have to do the best I can. What I have done with the word “faith” is to try to show you that faith in Truth is much larger, stronger, and very much more beautiful than “faith” in (how did you put it? oh, yes) as a “synonym for any old belief.” It is faith taken to the highest extreme. It is faith held steadfastly and proudly even when one is persecuted to the point of martyrdom simply for having it. It is faith that makes people so secure and so happy that they want to stand on a mountaintop and yell it out so that the whole world can hear.
Do I have faith that the sun will rise tomorrow? Well no, not really. I have faith that it probably will rise, I guess, even though I probably won’t see it because it rains almost all the time here so it will be covered up by clouds. Yet I will be able to sense its presence if it does rise because there will be light, although that light could be coming from something else. Using the word “faith” here is really incorrect, which I believe is one of your points and I concur with you on that. Instead of “faith” I would use “hopeful expectation” or something like that. Do I have faith that the sun will rise every morning for the next billion millenia? No and any “faith” I have that the sun will probably rise tomorrow is lackadaisical faith, easy to dismiss, weak, and lazy.
Do I have faith in God and His Church? Absolutely, one hundred percent, until the day I rest in Him and for all time to infinity. Yes, yes, yes. There is nothing weak or lazy about that faith. It transcends all other faith I may have. It is part of me, part of my soul, part of my essence, part of my being. It is Truth. It is.
I have told you I cannot discuss personal revelation. If you knew what I knew and have felt what I have felt you would have no doubt at all. This is true faith in God and His Church, huge, written in cursive letters, glorifying and praising God, deep, always present, and with me for eternity.
And if you can’t understand what I have stated above you will not understand my faith unless you experience something similar to what I have experienced. I pray that you do.