Cheap Gigabit switch will allow DHCP thru it?

[Bruce Labitt]

I'm looking to add another hdhomerun tunerbox to my myth setup.  I have 
a DHCP server running to give the existing tuner its IP address.  Can I 
add a cheap gigabit switch to add the other tuner?
Will the requests for IP address be routed to the server properly? 

How do I guarantee the tuners don't swap if the power goes down?  Does 
it matter?