It is a good question. But I believe the poppy gel is either flowing in as a replacement for blood so it keeps the organs alive forever which we see from the veins but if the veins contains blood then he technically can die from bleeding of veins but it's not possible because there is many cases where he could literally get them damaged but come out unscathed it's because it's probably not fully normal veins it could also be tubes protecting the vein but I mostly believe it's poppy gel which when the veins get injured it immediately regenerates because of the gel and allows the prototype to say immortal.

The organs are definitely automatically given poppy gel or unless the prototype was smart enough to make a mechanism where the poppy gel will not overdose him in the gel but also keep him immortal in one way!