No you don't need ASE neither to create a online or lan server! ASE is just like gamespy - it's a large list of game servers, for different games.. ASE just includes MultiTheftAuto
You can easily make a mta:vc server, for other users across the internet, without having ASE enabled... This way, only people who know your servers ip:port, can join (or people with port scanners - if you havn't password protected the server).
EDIT: Yeah you'r right IJsVogel - your answer sounds a bit better that way