i didn't use any screw until this very moment and almost all my panels are gone.  So yes you can. I did make my chainplates completely in glass epoxy, you don't need carbon for that. 

Panels? Do you have photo of your chain plates?

20241202_104425.heic

with the panels I mean the ply wood panels. I hope the picture is clear. 

I have dyneema rigging mostly. Yes the boats are sustained by glue. I have the designed bolts on my chainplates because  of possible local rot and then glue failure. This can happen behind the scenes. My 31' has water traps, so beware local rot. If you are building a boat designed for "plastic" like Sven Yrvind, then fair enough, perhaps mechanical fixings can be mostly replaced by lamination.

When glueing up, screws are indispensable unless you are able to use a vacuum press, and then you still need some.

That's based on 40 years pro woodworking experience.