Fast track Certificate or Diploma (in Business related) from a well known university

A distance learning course of no more than one month will almost never – possibly never – qualify you for alumni standing from a highly prestigious global university.

For example, you mentioned two short, non-credit certificates from Stanford. Let's look at the Stanford Alumni Association.

Membership General FAQ.

There's a list of benefits for Affiliate members including a STANFORD magazine subscription and a discount at Stanford bookstore. But there are key, networking-related benefits an Affiliate can't get, including "access to some regional events, most alumni clubs or the alumni directory." Affiliate Membership. You

There's a separate Stanford Graduate School of Business Alumni Association, but it looks like you wouldn't be eligible for any status with them for having taken a short online certificate course.

There are similar rules at other schools.