Great question. Currently no, but I've looked at a few options around this. It's something I would certainly like as well.
The main problem is that standard VST3 plugin parameters are fundamentally numbers, and expected to retain their meaning over time. For example 0-127 is a continuous parameter value for things like the track input level. Enumerated parameters like Quantize have values displayed as Off,Subcycle,Cycle,Loop, but those choices never change so the parameter value saved is just the the index number 0-3.
Sessions are more variable, they have user defined names, and they can be created and deleted at any time. To save those as numbers, they need to be assigned a number from 0 to 127 as they are created, and that number can't be reused for any other session, until the first session is deleted. Not a particularly hard problem, but I haven't gotten around to it yet.
You can designate one session as the startup session that will be auto-loaded whenever you launch Mobius, but that doesn't change based on the host project.