It can. That is why some of us do not do staggered hatches or why those that do staggered hatches often have a second incubator to use specifically for lockdown.
The idea of a certain humidity during incubation is that enough moisture evaporates so that the chick does not drown when it internally pips. The idea of turning during that time is so that the developing chick does not touch the inside of the egg and moisture evaporate directly from it so it would stick to the egg shell. In lockdown the chick is so big it is going to touch the sides of the egg anyway so you might as well stop turning. You increase the humidity so the membrane does not dry out and stick to the chick, expecially when it pips.
This is a simplistic view. I'm sure I don't know everything that goes on during incubation and hatching, but I think this is a good working hypothesis.
Different ones of us get different results with humidity. There are different theories for that, but if you read the posts, there is no one right answer for all of us. I cannot tell you what will happen to your other eggs in your specific circumstances if you increase the humidity during lockdown and hatch or if you choose to not increase humidity for the earlier set of eggs. You may do OK and you may not. I personally choose to not do staggered hatches because of this.
I wish you luck but can't really offer any advice.