If you've got the time to experiment, this is a good way to get a customized matched set. An easier way to get a good match is to buy a matched component system from a vendor. This assures that everything works well together, and generally comes with a guarantee. The media is optimized to work with the ink, as well as the laminate. There are lots of handy substrates on the market that will withstand the weather, but bond paper isn't one of them.
Unprotected paper absorbs water from rain, snow or fog, and rips easily in the wind.
Let's assume the ink lasts two years. If it's normal paper, the answer is going to be no. There is a large variety of durable products on the market now, including vinyl, Tyvek, polyolefin, and other plastics. Before discussing specific products, let's determine what makes a good outdoors medium. The first characteristic is found in just about any plastic-like material.