Yes, the game will ask you to update and won't let you connect to servers if you have an old client.
You can re-download whenever a new version comes out, but the better way is to install the itch.io app (it's like the steam app) and install Hunternet via the app. That way when I release a new version (usually once a week) the app will download a small patch automatically and you don't have to download Hunternet all over again.
A new version of Hunternet will be out for this weekend's play test. Among other things it introduces heat sinks (you can equip them to lower energy costs which makes your existing equipment more efficient and makes it harder to overheat). It will also include the first version of the shooting range.
Let me know if you have any more problems. I'm usually hanging out on the game's discord server and that is usually the fastest way to get my attention. Have fun, and hope to see you in the Hunternet :D