No. Studs runs in your browser and can publish straight to your Roblox account, so you can go from idea to a live game without installing anything.
When Studio is useful
Every finished run can be downloaded as a .rbxl file from the publish menu. Open that file in Roblox Studio to play your game before publishing it, or to make small changes by hand.
Changes you make in Studio stay in Studio. Studs does not read them back, so if you keep building in Studs, later runs will not include your Studio edits. Pick one place to work on the game and stick with it.