Yes, you will have full access to all latest updates after buying the game.
Download itch launcher for automatic update everytime you load the game. https://itch.io/app
If you can't download itch launcher, then you have to manually download the game again, then manually move the save file, everytime it has updated.
The development of this game is pretty fast, almost always an update per week on time, so I recommend using Itch launcher.