Are social networks typically good expanders?
Social networks typically have many vertices with just one or two connections to the rest of the graph. Such vertices will typically lead to a bad spectral gap. 

What you could hope for is good vertex/edge expansion for sufficiently large sets. However, if you have tightly-knit communities within the network, then again you would expect low expansion. 

I'm not sure if it quite answers your question, but the following empirical paper looks at exactly expansion-like properties in social networks. The answer seems to vary from network to network.
http://fragkiskos.me/papers/expansion_SNSMW11.pdf

I'm sure there is other work out there along these lines, possibly disguised using alternate terminology ("community structure", cut sizes, etc).