In a closed circulatory system, all of the blood stays within blood vessels or the heart itself.
Organisms that have open circulatory systems, such as arthropods, have hemolymph (a fluid that is essentially a mixture of blood and interstitial fluid). The hemolymph actually does travel in vessels for a very short amount of time, as it is leaving the heart. After this, it goes to the body cavities of the animal and directly bathes the tissues in the fluid in order to deliver oxygen, nutrients, etc.
Hemolymph moves throughout the body when the animal moves. Also, when the heart relaxes, hemolymph is drawn back toward the heart through ostia, or open-ended pores.
So to answer your question, yes, these animals can survive just by pumping hemolymph straight into the body. This is only effective because their body cavities are very small. In humans, an open circulatory system would never work because it would require an enormous amount of work to pump and circulate blood throughout our entire body cavity.