There's a bunch called the hash house harriers who did exactly what you're describing.
en.wikipedia.org/wiki/Hash_House_Harrierswww.hhh.asn.au/The Constitution of the Hash House Harriers is recorded on a club registration card dated 1950:
* To promote physical fitness among our members
* To get rid of weekend hangovers
* To acquire a good thirst and to satisfy it in beer
* To persuade the older members that they are not as old as they feel
Members often describe their group as "a drinking club with a running problem,"