Is there a way to seal a wood cabinet ?

Tighten the cabinet up. 

The prior suggestions will SLOW the deterioration of the plywood. That grade of plywood WILL deteriorate far faster than you want when exposed to weather. Sealing isn't something you can effectively do to plywood used for indoor cabinets.

First coat of poly or varnish, cut it with a thinner so it absorbs better, then proceed with at least one, if not more coats. Marine or spa grade.

I agree with oil field trash. Marine-grade varnish is your best bet. At least two coats, on every single part of it.

You are right.  Humidity will de-laminate that plywood fast. Extreme weather happens, and also fog, mist, drizzle (all which is 100% humidity) so right until you get freezing will this be an open wound.  Boat paints is probably your best defense.  Anything that is exposed wood is subject to damage by moisture.

A coat or two of paint and/or polyurethane would seem like good wheeze. 

I think I would use an epoxy paint in that location, it is the glue that will give way eventually.

I would recommend Minwax Helmsman spar-urethane varnish. It is designed for use outdoor and even on parts of boats. It has just a little bit of stretch to it so it can expand and contract with the wood as the temperature changes. Be sure to seal all parts of the piece inside and out as well as all edges. 

Thompson's Water Seal will do that.  and the sales guy at your local paint department may have other products that will also work well

Giving a coat of poly, stain, or paint will always add durability