Thanks for participating in the Forum! We do not recommend to use the Slingbox connected to a Switch, the Slingbox might not get connectivity. But you can use a wireless bridge or a power bridge like the SlingLinks.
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I have a large home network with 4-5 (I've lost count) Gigabit switches. They'are all made by 3com (in fact they're discontinued) but it all works fine. I can't see a problem if everything is running on the same logical subnet and you can ping the router from where the Slingbox is, etc. Don't use the fancy switches which have firewalls or state management and you'll be fine.
I was worried about the same thing because Sling's instructions say "plug the Slingbox into your router", yeah, right, my router is two floors up from where by satellite receiver is.