Does the phrase "logistically very difficult" sound correct in the following fragment?
Given that it would be logistically very difficult to conduct the experiment
The phrase "logistically very difficult" sounds fine, but depending on the context you might also use,
Since when you're describing an experiment as feasible, it would be generally understood that you're referring to the feasibility of conducting the experiment, you could probably simplify this to:
Also note, you could replace "not feasible" with "infeasible", but that's a much less common word.
It is grammatically fine.
It's semantically fine if the experiment would in fact involve logistics: coordinating people, processes and delivery of resources across a broad geographic area.
People misuse "logistics" nowadays as a synonym for "practicality", "feasibility" or "complexity", which it isn't.
It's also not related to "logic" or that work's Greek root "logos" at all; rather, it's related to the word "lodge" and its etymology.