Should Class I electric devices be connected to unearthed sockets?
In the US, the National Electric Code allows replacement of 2 pin sockets with 3 pin GFCI outlets with the ground unconnected.  They must be labeled as such, but they are considered safe for use with equipment with a 3 prong plug.  You could make the assumption then that a GFCI outlet with a 2 to 3 prong adapter with the ground unconnected might also be considered safe, but it's advisable to connect the ground as well: (Note that EMI may be an issue with no real ground, but the section below deals with safety.)

Replacing Receptacles to Meet the NEC

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The NEC requires receptacles installed on 15 and 20 ampere branch circuits to be of the grounding-type and it requires the grounding contacts of those receptacles to be effectively grounded to the branch circuit equipment grounding conductor [210-7]. However, the Code allows the installation of any of the following installations when replacing a 2-wire nongrounding-type receptacle where no ground exists in the outlet box [210-7(d)(3)], Figure 9/10:

(a) Replace the 2-wire receptacle with another 2-wire receptacle.

(b) Replace the 2-wire receptacle with a GFCI-type receptacle and marked the receptacle with the words “No Equipment Ground.”

(c) Replace the 2-wire receptacle with a grounding-type receptacle where protected by a GFCI protection device (circuit breaker or receptacle). Since the grounding terminals for the receptacles are not grounded, the receptacles must be marked with the words “GFCI Protected” and “No Equipment Ground.”

A grounding-type receptacle that is GFCI protected without an equipment grounding conductor is a safer installation than a grounding-type receptacle with an equipment grounding conductor (if GFCI protection is not provided). This is because the GFCI protection device will clear a ground-fault when the fault-current is 5 milliamperes (+ or – 1 milliampere), which is less than the current level necessary to cause serious electric shock or electrocution, Figure 10/11.

A grounding-type receptacle without a ground is a safe installation as long as the GFCI protection circuitry within the device has not failed from shorts and voltage transients. To insure proper GFCI protection, test the GFCI monthly in accordance with the manufactures instructions and if the GFCI test does not operate properly, replace the GFCI protection device.