The Poskim say, If you didn’t daven Shachris ,you may not go to sleep
in the morning unless it is more than a half an hour before Alos Hashachar.
R. Eliyashsuv zt”l said
Those who go to sleep before Alos Hashachar not having davened, should
make sure to do so, at least a half an hour before Alos Hashachar, otherwise
it would have been better had he not stayed up for the night altogether.
Staying up the night of Shavuos is a only a minhag Not going to sleep before Alos is a Halacha.