Seems rather easy, isn't it?
Let's see what's there in Execute:
So, it just packs every single coroutine it has in SequentialResult and execute 'em. No filters pipeline used, no routedMessage. None of your neat filters applied to these coroutines.
To be prrecise it is an Action Execute overloaded method that in simple case of SynchronousAction does the following:
namely calls preprocessor filters, delegates a call to method that might be returning coroutine, handles errors with rescue filters, calls postprocessor filters. That is a filter pipeline I am talking about.
Well, seems that Caliburn has everything I need. And all I have to do is just use it.