Yes, GrapheneOS has always offered OTA updates via the System Updater app. https://grapheneos.org/usage#updates It's set up to download and install updates automatically by default. Alternatively, you can install a signed update package via adb sideload. https://grapheneos.org/usage#updates-sideloading

Both the update client and the backend are open source, just like the rest of the system: https://github.com/GrapheneOS/platform_packages_apps_Updater https://github.com/GrapheneOS/releases.grapheneos.org