Would covering walls with a sound absorbing foam reduce the transmission of medium-high frequency fan noise?
Easier than sound-proofing a room would be to build a sound-proof box for the server using the triangular foam. Since it's a rack-mount server, just building some ducts for the front and the back and lining the ducts with the triangular foam you linked to above may be enough.

An even better alternative might be to replace the system fans with low noise counterparts.