I do not believe that the hairy covering on Jacob and the hairy costume of John the Baptist are connected in a significant way and I'll explain why. The disguise of Jacob is part of a motif running at least from Genesis 3 through 2 Samuel.
Examples of the "disguised deceiver" motif include:
Then the Lord God said to the woman, “What is this you have done?” The woman said, “The serpent deceived me, and I ate.”
Then Rebekah took the best clothes of Esau her older son, which she had in the house, and put them on her younger son Jacob. She also covered his hands and the smooth part of his neck with the goatskins.
she took off her widow’s clothes, covered herself with a veil to disguise herself, and then sat down at the entrance to Enaim, which is on the road to Timnah.
Although Joseph recognized his brothers, they did not recognize him.
And later examples include Saul (and others)
2 Samuel 28:8
So Saul disguised himself, putting on other clothes, and at night he and two men went to the woman. “Consult a spirit for me,” he said, “and bring up for me the one I name.”
As you can see from the above sampling of verses, the theme of the disguised deceiver quickly moves on from the covering of animal skins to other forms of disguise. Therefore it's plausible to see the animal hair garment as predominantly part of the disguise theme rather than as part of the prophetic costume theme.
In fact, if there is a connection between Jacob's hairy garment and Elijah's hairy garment, it makes the most sense that this is a (very) vague reference to belief in Jacob's role as a prophet, rather than as a reference to Elijah as a deceiver.