The service account is always sysadmin on its own instance. Here is an interesting titbit: Say that the account DOMAIN\SERVICE is used as service accounts for instances. Say further that you do xp_cmdshell sqlcmd
on one instance to the other. This connection will be made with the service account, as long you don't have a proxy in place. But you will not be sysadmin on the other instance. Despite that you are logged in with the service account.
At least, this is my recollection from the tests I ran quite a few years back.