Yes, and there was once a Tempest-qualified DEC VT100 terminal. Fine wire mesh over the CRT face, an RF-tight metal case, and fiber optic I/O. It looked much like a regular VT100.
The US military tests their gear for this. Their test facility: (http://www.epg.army.mil/e3tf.aspx) has RF anechoic chambers big enough for a tank. They're interested in both "can it be eavesdropped upon" and "can it be interfered with".
Modern electronics is much RF-quieter than older stuff. This is because so much of it has radios inside. If your device generates much RF hash, the WiFi, Bluetooth, and cellular radios will all have much-reduced range. In the early days of personal computing, some devices were very noisy. A Radio Shack TRS-80 and a Milton Bradly Big Trak toy would both crash if operated near each other. We're way beyond that now.
The FCC's requirements on RF noise from electronics helped a lot. There was much grumbling at the time from hobbyists about RFI compliance requirements interfering with their freedom to tinker. The FCC was right, though. Today, almost no consumer electronics interferes with other consumer electronics. You can use a cell phone inside a data center and receive clear calls. Cell phones themselves have several radios, all going at once.
This is a remarkable achievement in RF compatibility. For a sense of how bad it once was, see the Marine Radio Society, (http://www.radiomarine.org/), which has restored an abandoned ship-to-shore radio station in Marin County, CA. All the receivers are in one building. The transmitters are in another building, several miles away, to keep them from interfering with the receivers.
http://en.wikipedia.org/wiki/Van_Eck_phreaking is the means of essentially viewing everything on someone's screen via the EM the monitor emits. It is said that Mossad has a van eck device the size of a normal suitcase that can view monitors from across a street. I actually believe it.
The same can be said for keyboards and mice as well, especially wireless ones. The solution is a faraday cage.