Dave Paine
As Carol mentioned, Baltic Birch ply is not made with waterproof glue. If a crack opens in the paint, water will seep in and the ply could de-laminate.

If you are going to paint, then get plywood designed for outdoor use, or the special MDF used for signs.

The paint should protect from normal UV/rain. I do not think the Varithane on top of an exterior paint would help, and may not adhere depending on the type of paint. I like Varithane, but it will not stand up long for outdoor use due to UV.

There are special coatings for outdoor use. One is made by a company called Sikkens, brand is Cetol. I use this on a mahogany side light for the front door. This lasts a few years before recoating. This is not available in the big box stores. Need to go to a paint dealer and it is expensive, but works.