It's kind of complicated. The short answer is probably not.
There is a problem where users who got the game for free could lose access, so I'm not sure I recommend playing the demo if you already have the game. It depends on when and how you got the game.
If you received the game for free with the Itch.io app before the price change, and did not claim the game for free during the transition period between Nov. 15th and Dec. 7th, 2024, you still have a free copy and receive updates for free. Uninstalling the copy, or moving to a new computer, will make you lose access to the free copy of the game.
Sometimes, installing the demo in the Itch app seems to overwrite the free copy, which has made at least one person lose access. If you did not pay for the game or claim it during the free period, then I'd say you should skip the demo to avoid possibly having your free copy overwritten.
It's totally fine to install the Steam demo though, this is just a potential issue with the Itch.io app.