To me, that's fine if you're actually having a conversation (i.e. that chat window is likely to be in the foreground). It can be a case of using spare bandwidth to minimize latency, so to speak. But it's terrible if the thread is meant to be in async mode.

Overall, I think the problem here isn't the method of communication, per se. It's people placing unreasonable demands on your attention. Someone who came up to you in the middle of your break and started rambling a vague request would be annoying in the same way, even though the method of demanding your attention is different.