Yes. Mojang (now Microsoft) has explicitly allowed the distribution of old, unsupported alpha and beta versions for preservation. However, you cannot distribute the assets (sounds, textures) for commercial gain. You must own a legitimate Minecraft Java Edition license to play offline versions legally (though the launcher does not check for Alpha versions).
With the release of Minecraft 1.21 (Tricky Trials) featuring auto-crafters and complex archaeology, why would anyone want 1.0.16_02?
If you manage to launch it, you will find: minecraft java alpha 10 16 02 download exclusive
Release Date: Approximately Late August 2010 Preceded by: Alpha 1.0.16 (The Nether Update) Succeeded by: Alpha 1.0.17 (Infrastructure/Halloween Update Prep)
When Notch released the Nether in Alpha 1.0.16, players flooded the new dimension only to find it hostile in unintended ways. The 1.0.16.02 patch was a rapid hotfix deployed to address critical crashes and mob behaviors that were breaking the game. You must own a legitimate Minecraft Java Edition
Open the assets folder. Create a folder called legacy. Place the resources zip file (containing terrain.png, gui, sound) inside legacy.
Open your launcher. If you see "Alpha 1.0.16_02 Exclusive" in the list, you are ready to play. you are ready to play.
Pro tip: Set your RAM allocation to 512MB. Alpha was a 32-bit application at heart; giving it 4GB of RAM actually causes garbage collection crashes.