Would it be plausible for a large animal to transport nutrients through its body through digestive tubules in addition to (or even instead of) the blood? The specific system would be a system of looping tubules branching off from a pump situated at the outlet of the stomach. The tubules will also have to have some sort of orifice that can sense the nutritrition of the juices and let the depleted juices into the intestine. Would this system work for creatures larger than regular spiders and other such animals?
If I understood correctly, you want to know how large an animal can be with an open circulatory system (which will necessitate a "spider like" digestive system).
I'm thinking about the largest extant animals that fit the bill and my take for it is the giant clam. They can be 120cm wide (~4 feet) and weight up to 200 kg (~440 lb.). I would nominate other animals but then it came to me that cephalopods have closed circulatory systems, so the giant squid is out. Stupidly gigantic jellyfish and colonial animals such as sponges are also out because they don't have a circulatory system.
If you want an animal that is mobile, and specially non-aquatic, then you might have a problem keeping an open circulatory system. Large animals will use circulation not only for food but also for gas exchanges - Square Cubes dictates that tracheas and such are only useful up to certain sizes. That necessitates closing the circulatory system in order to keep it efficient.
We don't know for certain how the circulation for some cambrian animals was, but the Anomalocaris probably had an open circulatory system. It could grow up to a meter long (~3.3 ft) according to Wikipedia, but other sources say it could grow twice as long. It was an apex predator at its time, so it was probably quite active. Jaekelopterus was even bigger, at up to 2.6 meters long (8.5 feet, as long as MCU Thanos is tall) and probably had an open circulatory system as well. That might have been possible because back when those creatures lived, the concentration of oxygen on Earth's atmosphere and seas was higher.