So wouldn't mind trying this out, but the comments from Paizo folks seems to indicate that it just wouldn't work due to how slow PBP runs.
Maybe some people will run it just for fun? It's the only way I can play due to life circumstances.
My understanding is that there are seven mini-adventures in Doomsday Dawn, each of which will be allotted 2 weeks of time in the playtest. If you skipped straight to the last of the seven adventures that would give you 14 weeks to complete it, which might be enough time to be possible in PBP. However, you'd need to have an extremely motivated and active group that can maintain a high level of activity consistently across a 2-3 month period. This is a level of dedication that you're very unlikely to find by recruiting strangers on a public forum. If you have a group of extraordinarily dedicated players this should be possible, but anything less will likely fall short.