No, altitudes are sometimes measured in km, at least once you get beyond the Earth's surface.
From http://en.wikipedia.org/wiki/Hubble_Space_Telescope: Orbit height 559 km (347 mi)
From http://en.wikipedia.org/wiki/Olympus_Mons: Peak 21 km (69,000 ft) above datum
Yes, but the first is an altitude, the second more precisely termed an elevation. Good to have examples for both...
Altitude may be above Mean Sea Level (MSL) or above local ground level (Above Ground Level, or AGL) or even further definitions exist. Elevation is always Ground Level above Mean Sea Level. I believe Wikidata should only deal with the latter.
Alternatively, if sticking with Altitude a required qualifier would be need to distinguish which kind of altitude is meant.
Else a geolocation of a radiotower: with altitude = 400 m could mean that the ground is 400 m above MSL or that the top is 400 m about GL.
Gregor