Yes, NVIDIA stores your saved games on the GeForce NOW servers using your NVIDIA Account and also syncs your saved games to your digital store account so that your progress and achievements will be synchronized with other gaming PCs.
Note: You must have the cloud sync enabled on each game and digital stores for cloud saves to work.
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I signed up for a free trial a few days ago and tried to stream a game. First, got a "speed too low" warning which shouldn't be true, but it allowed to to proceed anyway. Then to stream a game, I was put in a queue of 60+ gamers which eventually changed 40+, but then it hung there for way too long before i lost interest. Maybe it was a busy time of day, but I might retry later. Not a fan of having to use chrome browser on steamdeck tho.