You can, but it’s going to break you in the long run (due to db size), and it adds hosting costs in terms of pageview, storage, bandwidth load.
It is true that there are two distinct forms of communication, and I definitely agree with this characterization:
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fast lane — chat, disconnected / incoherent words, ephemeral, lettin’ it all hang out, off-the-record
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slow lane — discussion, coherent sentences + paragraphs, permanent, on-the-record
At the moment, I suggest signing up for a free Slack account and getting a companion chat area. That’s a better strategy than contorting Discourse into a chat room – and Discourse has built in Slack integration.
(You could also experiment with plugins, but again: 
. Arbitrary plugins is an enterprise feature for our hosting. It’s difficult for us to dedicate internal resources to pure chat when it’s not really what we do and incurs an opportunity cost; it takes time away from working on other discussion features that have been on our roadmap for a while and definitely would deliver a lot of value to our customers.)
To be clear you can use anything to do anything. Whether it’s a good idea is another matter.