Short answer: Yes, they contain hemolymph.
Mammals are bled during slaughter by cutting a major artery in the neck. Molluscs (osysters are part of the mollusc group, along with snails, octopus and many others) do have a couple of major arteries (labeled Anterior aorta and Posterior aorta on the image below), but these are tiny, so trying to bleed one would be both very fiddly and destroy much of the form of the animal, so would be a waste of time and effort as I'm not sure that their circulatory system is under much pressure at all.
Like most shellfish, oysters are cooked whole and from alive, so the hemolymph should be present in the animal when cooked.

Image attribution: KDS444, CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0, via Wikimedia Commons