Praying the entire night in Ramadan is allowed. Unlike in other months. And would like to add that that 20 rakah of tarawih in the old times were prayed in like 4 pages per rakah, and thus extended from near Esha to a little before Suhur.
Now a days in Haram, this was done more or less by Tarawih + Tahajjud at night in the last 10 days, which extended from Esha to Suhur with a little break in between.
Now that everyone is praying himself, this is something to keep in mind.