I work wood, green and otherwise, and I think all would agree that putting a surface finish on recently harvested timbers will be a pretty frutsrating process. the main issue is that the moisture in the green wood will be moving to the drier surface and pushing any surface sealer out of the way to get there. Conventional wisdom is to let green timber air dry until it reaches a rough equilibirum with the atmosphere. The relative humidity will of course vary from area to area and seasonally, and equlibrium is also different for different species of wood. The Wood handbook, published by the US Forest Service and available for sale on this site has useful information on these points.
Sealing the ends of the timber immediately after harvest is important, however, because it will prevent overly rapid drying - and the resulting cracking and splitting of the timbers - during the drying process. If you could cut or purchase the timber, seal the end grain, and keep them covered but allow the air to circulate around them for a year or so before you built your structure that would be best. Otherwise I think they will tend to dry and split most on the sides facing the sun and wind.
Bottom line, if you can't coat the end grain, sticker and cover the timbers for a year before using so that they will be air dried, I would paint the end grain and build it, then wait a year or so before staining and sealing.