If I mount as remote samba (running on Linux) with Nautilus (sftp://) with a username and password will the permissions work as if I were on the remote system regardless of the local user name and the groups the user is part of ?
Samba is the Linux subsystem that handles Windows Networking (SMB/CIFS). SFTP is the SSH version of FTP.
Nautilus mounts both via GVFS. The permissions you'd have on the remote filesystem will depend on how the remote system is configured, and what remote user you use to authenticate to the remote system.
Unless your local system and the remote server get their users and group memberships from some centralized directory service (LDAP or the like), the permissions you get on the remote connection will likely be different than the permissions you have on the local system.
Further, the Samba subsystem can provide another set of permissions, and is not necessarily configured to synchronize those with the system user. In contrast, the SFTP permissions you get will be those of the remote user you're authenticating as when logging into the remote server.