Yes you can. In the s2 General options, look for Member Profile Options.
Then Redirect Members away from the Default Profile Panel.
Then you can use the s2 short codes to only display the edit option to specific member levels.
Pseudo Code: Allow edit profile level 2 or greater…
Show and edit profile info for Members who are logged in with an s2Member Level >= 2.
Let them know they can’t edit or whatever bla bla bla.
Note: Always test access with a non-admin account. S2 and WordPress handles security differently for Admins.