I can't remember when or where I saw it, but at one point I remember being able to fill a cauldron with rainwater.
Is this possible in Vanilla Minecraft?
To quote the Minecraft wiki:
A cauldron slowly fills with water when rained upon, if starting empty or with some water. This happens randomly, at 5% of the rate in which snow accumulates on the ground during snowfall.
Yes, it has a chance to fill it. In fact someone even built a machine that fills them when it rains and I suspect you could use them as a type of rain detector with a comparator.
Cauldrons do collect rainwater, however, it is only by chance.
A cauldron also has a chance to fill up with water when rained upon.
According to the Minecraft Wiki.