Yes, definitely possible, you will need to enable multi-org for that.
You will also need two Marketing Cloud API Users, one Service Cloud API user and on Sandbox API user.
Here is the outline of the connection:
PROD BU ---- MC PROD API User ---- Service Cloud API User
Sandbox BU ---- MC Sandbox API User ---- Sandbox API User
Read more about Multi-Org ...
Sandboxes cannot be Dev Hubs or own packages. To enable Dev Hub, you must be in your
Developer Edition, trial, or production org (if you’re a customer), or your business org (if you’re an ISV).
Sandboxes' refresh cycles are not compatible with being the owner of a package and its associated version artifacts, which are expected to have an arbitrarily ...
Hope your user have system admin profile, When you refresh S2 sandbox from S1 sandbox, you can login using S1 sandbox credential just replace the suffix part of your username with S2 name. Once you logged in then you can change email address.
Hope it answer your question!!