At least that's the strategy of one CosmoGirl research director, who advertised for a once-a-week babysitter ["Stay-at-home dad needs a break!"] on the CraigsList journalism grad student discussion section.
Hey! I, too, would like to employ an eager, over-educated, over-qualified aspirant to watch the kid for a few hours a week by dangling the faintest unspoken hope that I'll help them with their actual career.
See how it's done at Gawker: J-school job hunt: CosmoGirl needs you!
In one of Anna Quindlin's books, she talks about how that's exactly what she did when she was trying to break in at the New York Times -- she went through all the babysitting listings and got a job with Lawrence Van Gelder.
See: http://www.barnard.edu/alum/magazine/pastissues/spring03/spring03feature.html