Yes.
It's very normal imo. They have been in an alien environment, no doubt had unpleasant things done to them, they pick up on your stress, and of course they feel ill on top of all of that.
Unlike adults, children are unable to process and reason what has happened to them, so it manifests itself in upset and stress.
IME the worst (constant high pitched crying and being unable to settle) passes within in a few days, but the needing to be with you 24/7 lasts longer.
If you can, for the next few days have him constantly attached to you and bf him to his hearts delight. Play games and read books while he is on your lap, or lying on the bed together. He needs to know that you aren't going anywhere and that he is safe. It's bloody hard work though, make sure you have as much support from friends/family/husband as you can.
He will turn a corner, I just can't tell you when. But when you're feeling really stressed about your velcro baby remember that they need you and that it's not their fault.
Good luck, you can do it!
Much love to you and your ds xx