Yes, PILGRIM is a Scrabble word!

Letter values in Scrabble US: P 3, I 1, L 1, G 2, R 1, I 1, M 3.

Is it a valid word?

PILGRIM is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

someone who journeys in foreign lands
one of the colonists from England who sailed to America on the Mayflower and founded the colony of Plymouth in New England in 1620
someone who journeys to a sacred place as an act of religious devotion

Also: pilgrim father.