No, proliferate is not a triggered ability, though it can be part of one like on Martyr for the Cause
However, Think Twice is reasonable at smoothing out draws, but so is Ponder, and I think Ponder is better at the job for the most part
They can be in either non-foil or traditional foil
Despite being underwhelming from a power level standpoint, Grizzly Bears has been printed across over a dozen sets and even inspired numerous functional reprints, including Balduvian Bears, Forest Bear, Runeclaw Bear, and Bear Cub
For just three mana you get a decent 2/3 body, but the real value comes from that end step trigger that turns your lifegain into card advantage
I ended up producing a document that suggested five other possible ways to do it, each with several tweaks