No. A Shuttle plan covers only the Shopify store that subscribed to it. If you run a second Shopify store, that store needs its own Shuttle installation and its own plan.
Why each Shopify store needs its own Shuttle plan
Shuttle installs separately on each Shopify store, and Shopify bills each installation on its own. A plan you choose in one store's Shuttle dashboard is charged to that store and unlocks features only there.
Each store also keeps its own products, orders, reviews, connected Etsy shops and settings in Shuttle. Nothing you set up in one store carries over to the other.
Set up Shuttle on your other Shopify store
Install Shuttle on the other Shopify store. See Installing and accessing Shuttle.
Connect the Etsy shop you want to use with that store. See Connecting Your Etsy Shop to Shopify with Shuttle.
In that store's Shuttle dashboard, open Settings and choose Plan to pick a plan for that store.
Free trial and free plan on another Shopify store
The 14-day free trial is available once per store. A store that has never used the trial can have its own, even if your first store already used its trial.
The free plan's monthly allowances are also counted separately for each store.