EDITL This was in response to Dama.
No...
Ben would remember the Lost people if he saw them in 1977 because they were there in 1977. The Losties could not possiby remember being on the island in 1977 because they didn't go to 1977 until after they crashed on the island in 2004.
Say you time traveled tomorrow, to the year 1960. While you were there you bumped into your parents and told them who you were. Then you traveled back to tomorrow again. Tomorrow you would know you went there and saw your parents and they would remember you were there too, but the you of today wouldn't know that you were in 1960 because you did not do it until tomorrow.