If I write a query for example:
var query = (from a in this.Context.Addresses where a.Active select a.Name);
then is it correct to say
if(query.Any())
return query.ToList();
return null;
notice the query didn't have a FirstOrDefault() or ToList() so I am wndering if .Any() runs the query?

Yes - it has to, given that it's got to return true or false. It can't possibly do that without running the query.
If you're going to conditionally return ToList(), you'd be better off writing:
var list = query.ToList();
return list.Any() ? list : null;
... or I'd actually recommend that you just return query.ToList() anyway, as it's a lot easier to write code which uses an empty list than to have to special-case a null value.
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