Ballooning spiders

I was catching up on my viewing of the BBC's latest offering - South Pacific - last night and they talked of colonization of remote islands. One of the ways was by being caught up in typhoons, small animals and seeds, but they also mentioned the use of ballooning by small spiders. A little wander through the internet has demonstrated that this is true and that the spiders need to endure very low temperatures to do it, also that they need to be less than 1mg in weight and use enormously long silks as their lifting devices. But could they get into the stratosphere? I don't know - reports suggest 7000m and aircraft height, though the latter can be highly variable. If they did, would they survive and could they carry microbes with them?