You are right to ask for studies and here are some after a quick Googling:
In five experiments, we evaluated how secondary information presented on a heads-up display (HUD) impacts performance of a concurrent visual attention task. To do so, we had participants complete a primary visual search task under a variety of ...
pmc.ncbi.nlm.nih.gov
But we don't need these as you and I have been in situations where you suddenly realize that the brain has been in autopilot for a while and that the blinking or the non-blinking has not been processed.
I understand and share your opinion about the SW instructions but I think it is more an zero-to-hero instruction than a hud/no-hud problem.
Anyway, lets be safe in our diving and at least, here in SB, we are aware of all these perceptions-options and just that, I hope, makes us a bit more conscious of our limitations.