Saw a "V" formation of ducks fly into a cloud once, then come tumbling out of the bottom! Whether that was due to the downdraft or the lack of the ability to fly in cloud, I am uncertain.
The threshold of perception has nothing to do with it, however - the laws of physics apply to all of the Earth's creatures! While I am certain that birds don't have spinning gyros in their heads, whether they can sense the Earth's magnetic field to the accuracy required to stay upright is another question - and I doubt that they do - so my answer is "no".