Most likely yes, for log shipping you will have at least one folder where the transaction log backups persist. And the SQL Accounts used by the log shipped destination will need read and or write depending on which purpose the server is for.
That means at a share level the permissions will be set for the account(s) to access the share, if the account is changed to a new domain account and the new account(s) are not granted the relevant permissions on the share they will not be able to write \ read the backup files.
For mirroring it will depend on whether you are using a SQL Account or the Service account for connecting across the end points.
MCITP SQL 2005, MCSA SQL 2012