Like always,
the answer is "it depends"
From my own journey in the research, and based on no practical
experience thusfar, you can certainly leave the bark on BUT it will invite problems you wouldn't otherwise have. Insect infestation, and specifically beetles, are #1 - they will lay eggs under the bark (and may have already before you've harvested the tree) which hatch out to larva that eat the outer layers of
wood, tunneling as they go, creating weakness and entry points for fungus and other icky things. If you treat the logs, this might not be as much of an issue. The #2 problem is the fact that it will fall off over time, leading to a less than appealing look as chunks of bark slough off the dry, seasoned logs. I read of accounts where people glued this back in place using various techniques and glue types. #3 in the list of problems is that the bark may hold moisture against the wood where it would otherwise have dried out faster/stayed drier - this can lead to mold and premature rot (as well as invite more insect pests...they love dark, wet places).
So to truly answer your question, the requisite questions you'd need to answer would be "how long do you want the structure to survive, how natural/clean do you want it to be and do you care about what it looks like". It's a judgement call based on your needs. Me? I left the bark on all the logs I built my temporary (shooting for maybe 10 years of usable life) shed/wrap roundwood timberframing structure, but am peeling all the logs I plan to build my more permanent cabin framing with