I wouldn’t risk AWS closing the account.
It should work, but don’t know how would AWS view it.
"You may not use Amazon Lightsail in a manner intended to avoid incurring data fees from other Services (e.g., proxying network traffic from Services to the public Internet or other destinations or excessive data processing through load balancing Services as described in the Documentation), and if you do, we may throttle or suspend your data services or suspend your account."
"You may not use Amazon Lightsail in a manner intended to avoid incurring data fees from other Services (e.g., proxying network traffic from Services to the public Internet or other destinations or excessive data processing through load balancing Services as described in the Documentation), and if you do, we may throttle or suspend your data services or suspend your account."