Q:

How would a mains transformer react to unfiltered "Class D" PWM sinewave on its primary? 

Somewhat related to this question: How do I apply PWM signal to the primary side of a transformer to get synthesized sine wave at the secondary side? -  specifically "Choice 1":

However in my case I don't have control over the PWM side of things.  The characteristics are:

a PWM sinewave, waveform as above;
Vmax = 100V;
fPWM = 2kHz;
fsine = 50 — 200 Hz;
Transformer: cheap "E-I type" laminated core transformer for 230VAC mains (230 to 24VAC, 10VA) (not fixed in stone, see below);
The filtering inductor might be absent;
I do not have the PWM driver at hand, so I cannot experiment with it directly. 

The aim is to have some much lower voltage on the secondary, in the vicinity of 10—20VAC.  Pure sinewave on the output not required. 
I'm wondering whether the ordinary type transformer for 230VAC mains (which is preferred because of low cost and availability) can be used in this scenario, or special type is needed because of the non-standard input?  How would it react to this waveform?  Especially if the filtering inductor is omitted? 

A:

Any ordinary transformer with a 230 V, 50 Hz primary rating should be ok over some range of operation.  I believe the increased frequency related aspects of the iron loss will overtake the declining flux related aspects at some frequency.  Check the transformer temperature at full load on mains power and compare with operation in your application to avoid excess temperature. 
The transformer will work on the first try in terms of transforming the fundamental voltage of the output waveform to a lower voltage at the 230:24 transformer ratio.  The output voltage will be reduced by the series resistance and inductance that you can determine by testing the transformer.  Start by performing open-circuit and short-circuit tests at 50 Hz.  Step-by step instructions for doing that should be easy enough to find. 
You may be able to do some useful testing to determine the fundamental frequency performance up to 200 Hz.  You might also find representative data for similar transformers published somewhere. 
To determine the effect of your PWM waveform, you might be able to do a simulation.  Or do some calculations based on the Fourier analysis of the waveform.  You may also find some useful representative data for transformers with 50 Hz fundamental and various levels of load current distortion. 
Depending on the extent to which you can analyze the system, you might just use a 50 VA transformer for a 10 VA load. 
You would need the equivalent circuit of the transformer to determine how much series inductance it adds to your filter. 
I have some experience doing something like this at 60 Hz and below and much higher power levels.  Our main concern was avoiding saturating the iron at low frequency, but we could adjust the V/Hz to avoid that at the expense of reducing the torque capability of the motor connected to the secondary.  The transformer was sufficiently oversized to avoid saturation to eliminate any need to consider waveform harmonics. 
Regarding dv//dt
The effect of high dv/dt is a valid concern, but you have some margin in this application.  The question indicates the maximum voltage without any ringing is 100 V compared to the design voltage peak of about 340 V for the transformer.  The magnet wire insulation rating is likely to be considerably higher than that.  With electric motors, the problem generally only appears when there are voltage reflections due to transmission line impedance effects.  If the inverter is close to the transformer that would be reduced.