Is there a way to have admins that are logged in to wordpress not have to enter the password for password protected pages while browsing the website?

Since 4.7 you can filter the post_password_required function:

function my_admins_dont_need_password( $required ) {
    if ( current_user_can( 'manage_options' ) ) {
        $required = false;
    }

    return $required;
}
add_filter( 'post_password_required', 'my_admins_dont_need_password' );

Replace manage_options with whatever capability you want to use to allow users to skip the password form.