I use Multi Site for WordPress as well. When I upgrade from 5.03 to 5.1, I will get a 500 error on my Network Admin page, but each of my sites will still function.
PHP Fatal error: Cannot redeclare wp_cache_reset() (previously declared in /wp-content/object-cache.php:119) in /wp-includes/cache.php on line 267
Since I have fully transitioned to 5.1, I have to remove WP Total Cache in order to access the Network Admin Dashboards. Or I would have to rolled back to a version that is 5.03, then Total Cache works fine.