I am getting conflicting information as to whether or not you can sync Albums under the My Albums category?

Once you have enabled the iCloud Photo Library, also enable Sharing.

See >>> https://support.apple.com/en-ca/HT202786

Can you sync My Albums (the individual ones) across devices using icloud?

Yes.

Shared Albums can't be synced as the are not hosted in your iCloud space. They are only accessible via the iOS/macOS Photos apps.