Yeah. Since Stardew only has free patches, rather than paid dlc, you can update without any further costs. I had to use my phone's data over shared wifi because there wasn't an option to just use my phone as a hotspot (this was several system updates ago and I rarely have my console online so it might not still be the case) but the whole thing was very quick and simple. If you're using traditional wifi, it's even easier.
You can buy paid dlc for other games with the freebie account though. I bought Vergil as a playable character for Devil May Cry 5 through the playstation store on my PC, and then just downloaded it on my PS4 after going online and signing in. Later, when I updated to an ssd with more memory, I saved the dlc on a usb drive and copied it over rather than download it again. I had to go online once to sign into my psn account so they could verify I bought it in order to use it, but I haven't had any issues with it since.
I've never used any of Playstation's paid tier digital services, so I don't know how that works, but I wouldn't be surprised if you couldn't access the games anymore after cancelling the service. It's what you're paying for, after all.