Not exactly, because the situations are almost entirely different.
In the book, there is no Harpy attack. It is just a day at the fighting pits, when suddenly Drogon appears and causes mayhem, though he basically only just kills people in the pits. Dany jumped into the pits basically to both protect Drogon and to stop him from causing havoc. Although there was an obvious threat to the others there, it was basically from Drogon, so Dany was essentially helping by mounting Drogon and getting the hell out of there.
Contrast that with the show, where there was an obvious threat to everyone, but here from a hoarde of murderous Harpies. Dany has retreated into the pit with her protectors and close advisors, huddling and holding hands while they realize their impending doom. Drogon appears and basically saves the day, but (presumably) since the Harpies start attacking Drogon, Dany mounts him to ride him away from danger...leaving all of her protectors and advisors to the remaining Harpies. The odd thing is that plenty of Harpies were brave enough to start attacking Drogon, but once he flew away, they all just...ran?
Just weird. The further the show gets away from the books, the less they seem to be able to handle the complexity of the world they created.