Yes, I'll move things along when I see fit. I don't think hard and fast rules are necessary but if I keep coming back to a game a day after the last post and find things are waiting on a particular player habitually, I'll intercede with an increasingly heavy hand. This could include having players take double turns or go full defence or moving role play encounters off camera or splitting the timeline as needed, but I won't lock myself down with set rules at this point.
If it looks like the game settles into a pace of its own and it works out to 3 or 4 significant posts a week, I'm fine with that too but I would prefer a faster pace.
I personally check my games at least twice a day and can do combat updates at work and at home so major GM updates should be every day or so as needed.