You are probably right. The Christmas Tree was imported into the celebration of Christmas by Martin Luther in Germany. He used the tree to support candles, which when lit represented the stars on the night of the Holy Birth.
Whether it was a previous pagan symbol I neither know nor does it matter. But no, I would guess Puritans had not picked up on the custom.
I believe the modern interpretation of Santa as the 'jolly old elf' came from the text of "The Night Before Christmas", and from Thomas Nast's illustration of the poem.