Culturally, caffeine and pizza are part of being a programmer. While it doesn't make for good main site questions (10k link) coffee, tea and other caffeine delivery mechanisms are a documented part of what it is to be a programmer for a significant period of time.
As noted, this is such a culturally significant part of the desk of a programmer, that it is part of the site's design. Think geek has coffee mugs as a major section of the site.
As noted on the Community Promotion Ads - 2015 you will note the wording:
This is a method for the community to control what gets promoted to visitors on the site.
This is a method for the community to control what gets promoted to visitors on the site. For example, you might promote the following things
- anything else your community would genuinely be interested in
The goal is for future visitors to find out about the stuff your community deems important. This also serves as a way to promote information and resources that are relevant to your own community's interests, both for those already in the community and those yet to join.
If the community is honestly interested in the culture of caffeine intake, then promoting that stack exchange site is well and good. Its an advert on the side of the page - not a main site question.
If, however, the powers that be suggest that this shouldn't be the case, I would urge them to get the requisite 125 reputation, participate on the main site and the community here, and vote on the answer. I would similarly encourage them to do the audit of all of the other graduated sites and ask themselves why Health.SE is advertised on Gaming and Cooking and Space.SE on Skeptics and then ask if its really worth the trouble of going against the community when it has reached a consensus of what other things they want to advertise given the guidelines we are provided with.