Is it possible to change the password of a SQL Server service account that is used for not only on the publisher server but the 6 subscriber servers as well without seriously affecting merge replication? I'd like to avoid (or at least be forewarned of) any potential issues because replication is not my strong suit and I hate troubleshooting it.
If the same username and password is to be used on all servers, you will need to make that change on all machines, or rather the replication agent jobs.
If you change the password but miss one of the subscribers, replication will not break. However, it will fail with login errors when the subscribers attempt to connect to the publisher and the password hasn't been updated on the subscriber. As soon as you update the passwords on all subscribers, they will run again without error.
This is a typical scenario for any password change, regardless of if replication is involved or not.
It may be prudent to consider updating your security policy for replication/service account usage and deploy dedicated accounts for this topology instead of using the service account multiple times. This is a security best practice and would allow you to increase the security of your systems.