You should be able to. You can find out if the current user is a site admin using REST then use CSS to hide the See All link. I do not have an online farm to play with right now to get the CSS but here is the code I use for admin checking on the client. Put it in a Content Editor Web Part on the list.
_spBodyOnLoadFunctionNames.push("loadPage"); //ensure the core.js is loaded onto the page before executing
function loadPage() {
var call = jQuery.ajax({
url: _spPageContextInfo.webAbsoluteUrl + "/_api/web/currentuser/issiteadmin",
type: "GET",
datatype:"json",
headers: { Accept: "application/json;odata=verbose" }
});
call.done(function(data) {
var isSiteAdmin = data.d.IsSiteAdmin;
checkActiveUser(isSiteAdmin);
});
}
function checkActiveUser(isAdmin) {
if (!isAdmin)
$("input[id$='id of control without GUID']").css('display', 'none');
//or $("input[id$='id of control without GUID']").hide();
//your css to hide the control here
}
This should work for you. Let me know if it works, or if you have any questions. Good luck!