Well, such a challenge seldom go untested. The same NIST group that made that time-keeping advancement has now reported a test of GR using such a device (like open for free only for a limited time)
General relativity states that time speeds up for objects as gravity weakens. To demonstrate this, Chou and his colleagues raised one optical clock 33 centimetres above another. The slightly lower gravity at that height meant that compared with the reference clock, the raised clock ticked with a fractional boost in frequency of 4 × 10–17, equivalent to a gain of 90 billionths of a second over 79 years.
To demonstrate special relativity, which says that time slows down for moving objects, the researchers jolted the single atom in their optical clock so that it oscillated at relative speeds of less than 10 metres per second, or 36 kilometres per hour. This time, the clock's ticks seemed to drop by a fractional frequency of almost 6 × 10–16.Amazing work!
 C.W. Chou et al., Science v.329, p.1630 (2010).