This should work, though I don’t know how resolutions might affect the output, you may have to lower your resolution in the console menu if it isn’t displaying properly.
If you have any sort of budget it may be worth checking your local stores for a small used flat screen instead of an adapter like this. I’m saying like $40 is possible. Almost anything with an HDMI port will look better than running though an adapter to crappy composite cables. Text in most modern games is going to be almost unreadable on that old TV.