Will no oil pressure make rocker arms come off valves and lash adjusters?

Yep, if the engine has no oil pressure for a period of time the lifter will collapse and cause excessive clearance in which case the roller fillor will get kicked off the camshaft position.

Here is a video that will help you see what I am talking about:

https://youtu.be/XRdG1ZEUSAc?si=eKPzaJjDGK0bbScS&t=1439

Please upload pictures or videos in your response to any problems so we can see what to help you with.

Yes, it could as the lack of pressure could let the adjusters collapse and then the arms are loose so they could come off. However, if there is no oil pressure at that point in the engine, I would be more worried about the damage it is doing to the bearings.