Sometimes it is useful to have e-mail address like
randomnumber identifies the conversation between a robot such as a mailing list server and a user. Is this possible with Microsoft Exchange?
Out of the box no.
You could develop an event sink that does the routing for you... This might get you started.
While the short answer is no, when the need arises and I don't wish to use one of the many web based providers of disposable email addresses I simply create one, use it and delete it when done.