Yes it does. Depression is is strongly correlated with guilt and insomnia since both are indications for depression. There are actually many psychological studies which proves this, but you may read about in Huffington Post:
Insomnia is often related to depression or anxiety. People with depression may have early morning awakenings and spend more time ...
Before that scene Will was just trying to sleep by covering the window and this time he even dragged a table in front of it to cover the whole light:
That is the time Rachel comes to Will's room due to the complains of other resident of the hotel:
And then Will told the whole story of how he fabricated evidence to help convict a pedophile he was certain ...
Dormer is a good man at the core, though he has done bad things with good intentions. He ultimately wanted to be held accountable, even if he couldn't quite admit it to himself until the end. The insomnia was a metaphor for his guilt.
It's likely he saw a young, idealistic version of himself in Ellie, and did not want her to become corrupted.