Is it Okay to Appear Constantly as Offline but Reply Back Instantly?
It's okay to work as you please.
I personally consider communication applications (email, messaging, chat, ...) as a distraction and I prefer to leave them closed, which goes further than appear[ing] constantly as offline...but still reply[ing] &quot;instantly.&quot;
You are free to define your own communication strategy. (Assuming you aren't mandated otherwise.) Of course, your strategy impacts others and some adjustments may be necessary.