I can confirm Godzilla does appear in the movie, but I don't know if Godzilla also appears in a post-credit scene, which is heavily speculated.
The official credits for Kong: Skull Island lists:
Characters of “Godzilla,” “King Ghidorah,” “Mothra” and “Rodan” created and owned by Toho Co., Ltd.
It's possible the Kong: Skull Island post credit scene references the Godzilla sequel, which is Godzilla: King of Monsters, which looks to feature the above listed Kaiju.
The director on Godzilla 2 recently seemed to hint at a Kong: Skull Island post-credit scene reference as well.
As Kong: Skull Island is set in the past (Vietnam War era) – before the 2014 Godzilla movie – it's possible the Kong: Skull Island post-credit scene could be featured in the present tieing into Godzilla: King of Monsters and also setting up the 2020 Godzilla vs Kong Kong movie.
I'll also say since Kong: Skull Island is set in the past, don't expect a big Godzilla scene or reveal in the movie as I'm told it goes by pretty quick. Guessing the post-credit scene is a bit more.
A Kong: Skull Island clip also references "Monsters exist."
"Kong: Skull Island" hits March 10th.