Even if it's not about anxiety, why waste people's time and attention with needless messages? At the very least it's as rude as constantly being late for meetings - a sign that the late-comer doesn't value the other people involved.
I rather appreciate a nice hello and a little chat before someone drops a big request on me. It makes my coworkers seem human and gives me a nice break. If I'm too busy for that, I politely let the other person know that I'm too busy for smalltalk.