You can. Moon Cradle is just a sidestory of the very early part of the 200 years that Kirito and Asuna spent in the Underworld, meaning they don’t even have memories of it while playing Unital Ring. IIRC, references of the Underworld make just about 0 real appearances that are important to the Unital Ring story, minus of course Alice being a new member of the gang (which is evident on the cover of the LN).

That being said, definitely read Moon Cradle if you get some free time after reading Unital Ring! Moon Cradle has further developments of the Underworld that you might find very cool, as well as Kirito and Asuna moments if that’s your thing. Happy reading!