No, the poison ivy blisters are the caused by the body's natural allergic reaction to the plants. If the blisters break and ooze, the fluid does not contain the oil that causes spreading.
The rash-causing oil, called urushiol, from the original contact with poison oak and poison ivy will continue spreading (unless removed) for the first one or two days. It is found in in all parts of poison ivy, oak and sumac plants whether dead, dormant or thriving.
If new areas of rash appear after three days, and you have not been in contact with the plants, you are most likely getting re-exposed to the oil from contaminated clothing, tools, or even your cat or dog.