It will if it's DRM-free. The login check is an optional call that the developer has to intentionally use. Usually if you're a small developer releasing a DRM-free game you'd make your game degrade gracefully if Steamworks doesn't work, so you can publish the same builds on Steam and on any other store.

99% of games that use that sort of protection can be cracked in about 5 minutes by simply copying a steam emulator library into the game folder.