What would be the 'pros' and 'cons' of applying for the café job, just to get an 'in' with the company?
Excellent answers already, I just want to add to the cons and mention something that seems to have been missed. Cons first.
The job you want may never eventuate, and the 'in' is unrelated and of dubious worth if any at all. People do move sideways in companies but usually in fields where they have proven an ability to change roles. Whereas you're not even in the same building or interacting with the people it would be valuable to in terms of changing roles.
A huge con is that it's not a job you want to do. This can lead to frustration, apathetic work ethic and all manner of negatives with nothing except a nebulous 'in' to offset it.
But by far the biggest con is the waste of time and effort, because there are better ways. You would be better off gaining relevant experience in something related to the role you want.
Lastly your idea of an 'in' has issues. There are two types of 'in' that are widely used and useful for what you want.
You network with the people you would be working with and impress them as someone they'd like to work with and someone who could do the work. Not particularly hard if you're in close proximity. This is the grass roots referral.
Secondly you demonstrate competence to management and come in through that avenue. This is trickier and may include some shameless 'yes man' stuff. But it's widely used.
Just working for the same company as the role you want is nowhere near as good an 'in'.