Definitely.
I learned by watching my aunt neglect herself for years while watching over my grandmother that when you neglect yourself, you ultimately can't be the best care provider...she finally found respite care, and then ultimately my grandma had to go to a more appropriate home for her needs...to me, the difference here is only age (and specific needs, of course). My aunt chose the home for her mom out of love and care, and that's where you'll be coming from too.
We just went through a similar thing last year with MIL. She is very old, 90, and physically failing. She requires help with mobility, bathing, dressing, pretty much everything. Although SIL wanted to take her to her home, DH & I strongly urged to consider a nursing home. We live 400 miles away, so we are no help at all. I had a frank talk with SIL about the meaning of taking care of a dependent adult 24 hours a day. My words were "You're life will never be your own again. Your marriage will be affected, your friendships will be affected. You will never again have a spontaneous weekend away, go on a cruise, or have guests in your home without having to make arrangements for your mother. I don't think you fully understand what your taking on." Ultimately, we prevailed and MIL moved into a very nice nursing home about 6 miles from SIL. DH calls his mom several times a week and SIL stops in about once a day to visit. It's the best of both worlds.
I liken this decision to the one we are forced to make now. We have no relatives or friends who are able or willing to help with him. BIL recently had a tantrum while we were visiting them and blurted out "You need to move back down here and HELP YOUR SISTER take care of her mother. It's not fair!" DH eyed him carefully and said, "You're right, it's not fair. I tell you what, let's negotiate. We'll sell our house and move to Florida. We'll take a week taking care of Mom, and YOU CAN TAKE A WEEK WITH CHRISTIAN."

Yeah, he backed right off of that...
Minky,
They recently got in a new resident from a situation similar to yours. DD comments on how particular the mother is about his clothes, food, care, etc. and I reminded her that this must have been a very difficult decision for the mom and it is not easy to all of a sudden turn over care of your special needs child to someone else. It just goes against the grain of motherhood. So DD understands and is cutting the mom some slack! But the mom is there quite frequently and they do take him home on some weekends. DD has also developed special relationships with the families of her residents. They are grateful because they know their family member is being treated well and with respect, they are happy and healthy, and the family does not have to shoulder the load alone. Then the time they do spend with the resident is more quality time as the family is not so exhausted.
This is exactly how I envision it for us. I'm pretty overprotective of Christian so I will have to guard against being a pest.

I think we will enjoy him so much more when we can be relieved of the daily physical burden and concentrate on just being with him.
I had a long talk with DD17 today, to bring her up to speed. She as very mature and understanding about the plan. I didn't think she would be upset,that's not her style. She's very pragmatic. I made sure she understood that we wanted to place Christian so that she and DS23 would not have to take him into their homes and be responsible for him, especially when they'll be raising a family of their own. I told her that I expected the two of them to see that Christian has Christmas, birthdays, Thanksgivings,etc, and warm clothes, dental work, sensible shoes, and the occasional toy. And she agreed that she would do that.
I know that's a lot to put on a 17yo, but I felt it needed to be said. I want her to go off to college next year with the knowledge that we are not only taking care of Christian,but we're taking care of her and John in the long term.