There is a rule in Hollywood that any events that do not add to the story should be omitted. For example there is no point in showing the detectives traveling to the suspect's house if nothing happens in the car, just show them arrive at the door. Or better yet, just jump to them questioning the suspect in their home. Screen time is precious and so is space on the page.
The inverse is also a Hollywood rule: If it isn't in the script then it didn't happen or it doesn't matter. Did the detective have a sister? If we never met her then s/he doesn't or it doesn't matter.
So the fact that it is mentioned strongly suggests (and to my mind establishes) that the blessing was significant.
But what is the significance? Well one might surmise:
- Jakob is shown to be greater than Pharaoh:
Heb 7:7 It is beyond dispute that the less important person is
blessed by the more important person.
- Jakob was "pursuing peace with all men"
Mat 10:11 And into whatsoever city or town ye shall enter, enquire
who in it is worthy; and there abide till ye go thence. Mat 10:12
And when ye come into an house, salute it. Mat 10:13 And if the
house be worthy, let your peace come upon it: but if it be not worthy,
let your peace return to you.
Psa_34:14 Depart from evil, and do good; seek peace, and pursue it.
Heb 12:14 Pursue peace with everyone, as well as holiness, without
which no one will see the Lord.
- Jakob was being grateful and returning a blessing for Pharaoh's kind immigration policy. This would have likely been a custom - to bless those who bless you:
Gen_12:3 And I will bless them that bless thee, and curse him that
curseth thee: and in thee shall all families of the earth be blessed.
What is key to the discussion is that blessings had power, as we see in the frequent and somber references to the practice:
Gen_27:31 And he also had made savoury meat, and brought it unto his
father, and said unto his father, Let my father arise, and eat of his
son's venison, that thy soul may bless me.
Gen_27:34 And when Esau heard the words of his father, he cried with
a great and exceeding bitter cry, and said unto his father, Bless me,
even me also, O my father.
Gen_27:38 And Esau said unto his father, Hast thou but one blessing,
my father? bless me, even me also, O my father. And Esau lifted up his
voice, and wept.
As an example of a blessing at time I'm quoting Isaac's blessing of Jacob (who he thought was Esau):
Gen 27:27 So Jacob drew closer to kiss him. When Isaac smelled the
scent of his son's clothes, he blessed him and said, "How my son's
scent is the fragrance of the field, that the LORD has blessed. Gen
27:28 May the LORD grant you dew from the skies, and from the fertile
land; may he grant you abundant grain and fresh wine. Gen 27:29 May
people serve and bow before you; may you be master over your brothers;
may your mother's sons bow before you; may anyone who curses you be
cursed; and may anyone who blesses you be blessed."