Yes. However, such positions are not common, because they rely on a pre-allocated pile of money being dedicated towards FLOSS.

When I was at Oregon State University, I worked for the Open Source Lab; you may recognize them as an option on your distro’s mirror list. During part of that time, I worked for the Open Source Education Lab, an outreach program which was funded by a grant through the College of Electrical Engineering and Computer Science (now the College of Electrical & Computer Engineering). This grant funded some get-togethers on campus, the local Linux Users Group, and some one-off interactions like giving talks to undergraduate classes about how to use FLOSS software.

But, when the grant ended, so did OSEL. OSL and the LUG are still around because their funding comes from OSL tenants and LUG club members respectively, but they are not focused on outreach and advocacy.