Plug adapter voltage rating
A direct mechanical adaptor such as this, with NO LED indicator, if designed anything like properly, will be safe on 110 VAC or 230 VAC. 

An included LED which is designed to operate on 110 VAC will PROBABLY survive on 230 VAC but may not. Such a LED probably uses a series resistor.
PER mA of LED current a series resistor dissipates about 60 mW on 110 VAC and 120 mW on 230 VAC per mA of LED current, but when the voltage is doubled the cureent will about double, so energy dissipation in the resistor will rise by about a factor of 4 and in the LED by 2+ times*.
 (It will have a fwd series diode or reverse parallel diode across the LED so power will be consumed only during a positive half cycle relative to LED -ve.)  

As the resistor dissipation double on 230 VAC relative to 110 VAC the resistor power dissipation may cause failure on 230 VAC. Also, there is a chance that a resistor that operates OK on 110 VAC will fail from voltage breakdown (regardless of dissipation) on the higher voltage. 

The LED MAY use a series capacitor. The voltage rating of this will determine 230 VAC survival.  

Any series or parallel diodes used need to withstand peak 230 VAC voltage. 

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Resistor dissipation:


If LED voltage is say 3V at X mA and 4V at 2X mA then ~~~=:  


Say I_LED is designed at 2 mA at 110 VAC.
I LED will vary with AC waveform point. Assume Veffective is 110 VDC but it probably won't be.
R = V/I = (110VDC -3V_LED)/2 mA = 53.5k
Very non critical - say 56K used.
Power_R = V^2/R = (110-3) ^2 / 56k = 193 mW. 
This is for a full cycle so 1/2 cycle power = about 100 mW

At 230 VAC if VDC mean = 230 VDC then 
I~+ 230/56K = 4.1 mA.
As Vf_LED at 4.1V ~= Vf at 4V.
I actual = (230-4)/56k = 4 mA.
ie the LED voltage has minimal effect on current BUT the current doubling MAY damage the LED.
Power-56K is now about 230V x 4mA x 50% duty = 460 mW.
Ideally a 1W + resistor with say 400 VDC rating should be used.
If a very small SMD resistor was used that usually didn't fail at 110 VAC it may well fail at 230 VAC.
The above figures are for 2 mA LED current. Scale approximately linearly with current for other currents.