Not... quite, unless your rotational string would already have been perfected (e.g., Twin Snakes and Demolish are each refreshed only just before they'd drop -- ideally such that Twin is snapshotted onto the animation and you briefly see the buff disappear before reappearing and Demolish is as late towards the next global DoT tick as possible).
In practice, it will often work out that way depending on your opener, but you'll still end up with an extra Opo-opo and a better optimized Twin and Demo from each Solar.