I don't understand the question. You mean convert the 230Vac back to DC via SMPS? And you're wondering if that load will change the harmonics on the inverter output to even harmonics? That depends on the type of SMPS you use... but in general I don't think it would "change" the harmonics from odd to even. There's no reason to assume that the odd harmonics will go away, but new harmonics may appear or grow stronger.
Basically he means that any waveform which is symmetrical around its average value (zero for a pure AC signal), there can be no even harmonics. This can be proven from the fourier series by construction. I don't think it answers your question though.
I know it sounds like abit weird setup. But to simplify it its:
12Vdc->230Vac->48Vdc->sensor system.
On the sensor outputs i see the even harmonics of 50Hz. So i see 100Hz, 200Hz, 300Hz. But not the 50Hz,150Hz,250Hz.
If i analyse the 230Vac output i see the odd harmonics(as of the reason you wrote with symmetrical around zero). So im having a hard time figuring out why i see the even harmonics on my sensor output.
Because if i use the NET supply 230Vac->48Vdc->sensor system, i dont see the even harmonics(100,200,300...), but i see the odd harmonics(50,150,250...)