Yes. There are two different kinds of syncing going on, and it helps to know which is which.
Your iCloud account — between your own devices
Everything you keep in Yarn Squirrel — projects, notes, photos, counters, stash entries, bits and bobs, imported patterns — travels between your iPhone, iPad and Mac through your private iCloud storage. No account with us, nothing shared with anyone.
This works whether or not you use Ravelry.
Pattern PDFs are the one exception, because a file lives outside the app’s own storage. Which way you chose decides whether they follow you automatically — see Where Yarn Squirrel keeps your PDFs.
Your Ravelry account — your library, stash and projects
Separately, if you’ve connected Ravelry, your library, favourites, queue, stash and projects come down from there. That’s why signing in on a brand-new device fills things in on its own.
Why a new device fills in gradually
iCloud delivers your data in the background, in batches, at whatever pace the network and the system allow. So a new iPad may show some projects before others, and a large library can take several minutes to arrive in full. Leaving the app open on Wi-Fi is the quickest way through it.
If something still looks missing after a while, opening and closing the app gives both kinds of sync another chance to run.
If iCloud isn’t available
Yarn Squirrel keeps working. It falls back to storing everything on the device alone, so nothing is lost — it just won’t travel to your other devices until iCloud is reachable again. This is what happens if you’re not signed into iCloud, or if iCloud is unreachable when the app starts.
Occasionally the app has to be restarted before syncing picks up again after a bad start. You’ll see the current state under More → Settings.