It’s absolutely possible as - like already mentioned in the comment above me - you get “JOIN” messages on the IRC connection to the chat which you can then use for whateer suits you.
A more easy solution would be (and many streamers actually do this) is to have the chat open on your phone or tablet and having that somewhere in sight. As you really only need to see people that are actuall being active chat (“let lurkers lurk”), that should do just fine.