I cannot speak for those industries as a whole, or what would be accepted in papers, but to your question whether 'treating time-dependent data series of microbiological parameters like a qualitative result' is valid, I believe the answer is yes. If you can build an empirical model to explain the data you see from your process, and you can be confident that it is valid for the conditions you are trying to estimate, then I think could build a useful model. You must be careful though. As you referenced, a linear model which has a great fit over part of your data might not be valid when extrapolated past either end or your existing data, thus you need to be careful about what model you use.