Living animals with immune systems are the only types of organisms which can effectively host pathogens such that they can be communicated. Even your example belies the problem: pus is produced by the immune system destroying bacteria, it isn't a bacterial colony itself.

In an a bioreactor where no immune system exists, there can't be a latent infection: there's no immune system! If it can infect and destroy what's growing, then it'll infect and destroy all of it. It isn't going to look like tuna meat after that.

Isn't it possible for the pathogen to be limited by accumulation of its own waste products or depletion of specific nutrients before it destroys the whole sample, or for the meat to be harvested before the pathogen has finished propagating?