Yes it could be estimated, both with or without a random effect, but does not have to. This can be valuable when you want to fit, for example, a zero-order process, so you can just provide the amount you are aware will enter the system and the profile and let the duration be sorted out to optimize the fit. For complex absorption processes such as tablets with release profiles or intramuscular injections this is a great way to estimate such processes. In such cases, as NONMEM suggests, estimating both a nominal duration with a random effect can be valuable, however if there isn’t that much information about the absorption process sometimes this is not feasible and you can only use a fixed effect (though STAN it would probably be reasonable to apply a reasonable prior based on physiochemical/in vitro characteristics, given it is more flexible than nonmem)
or like in this case with Vanco, everyone just gives a 1 hour infusion, do rather than calculating the rates for each individual, it can just be hard coded.
The rule of thumb will generally come back to physiology and mechanistic plausibility. If you have a intramuscular injection that is injected in the glute for lipophilic (fat loving) compound, it stands to reason that you could have gender differences, and will almost certainly have differences between patients based on their body composition near the injection site. A morbidly obese woman (women have slightly higher fat contents) vs an athletic man could have drastically difference release profiles. On the flip side, some new microsphere formulations are really good for controlled release that don’t vary much between patients (maybe only 10%), in that case, having no random effect would be a reasonably simplification.