Disclaimer: I did use a hacking software for these tests. Please let me know if you would prefer something more authentic, and I can convert this to a comment.
First, I started by hacking myself 500 fossils.
Next, I went and revived 86 of them, and checked my Pokédex. I’ve unlocked form for for female, but no shiny. I checked my PC and no shiny.
In my hacking software, I changed one of the Tirtouga in my PC to be shiny. I opened Alpha Sapphire.
I opened my Pokédex immediately, and I have unlocked the shiny form.
Tl;dr I tried it out myself, got bored, turned one of the Tirtouga I revived that was in my PC into a shiny, checked my Pokédex, and it was shiny in the forms. Theoretically, you should be able to view shinies from your dex even when immediately sent to your pc legitimately.
I hope this helps!