No it doesn't. But there is every reason to expect those features would have been added at some point if VBScript had been more popular.
Indeed, if we look at VBScript's cousin, VB.NET, we find both first order functions and async functions, at least in its newer versions.
(Keep in mind that those features weren't present in older versions of JavaScript either. Async functions were only added in ECMAScript 2016. First order functions have been there from the start, but ECMAScript 2015 greatly improved the syntax for anonymous functions with its introduction of arrow syntax.)