No, Unturned was not originally a ROBLOX game. It was created by a ROBLOX game creator.
Unturned was not originally a ROBLOX game.
But it almost was...
Unturned was created by Nelson Sexton, a user who created extremely popular games on the ROBLOX platform under the username DeadzoneZackZak. One of Nelson's most popular ROBLOX creations was a game called "Deadzone" (which was a very similar to another popular game from that time, Apocalypse Rising).
After the massive success of Deadzone, Nelson announced that he was going to create a sequel to Deadzone titled "Deadzone 2". This is the game that eventually became Unturned, and it is why the concept and mechanics of Unturned are very similar to those of Deadzone. Nelson used his knowledge of Lua scripting and Java programming to build Unturned in Unity instead of the ROBLOX game engine, which all of his previous games had been in.
When Unturned initially released on Steam, many of DeadzoneZackZak's fans began testing and playing the game, sharing it with friends, and posting videos of it online. This is what gave Unturned its initial boost in popularity and lead to its early widespread recognition.
So while Unturned is a spiritual successor to a ROBLOX game, and it was created by a developer who gained recognition from ROBLOX, and the idea originally was for it to be a ROBLOX game, Unturned never was a ROBLOX game itself.