Javier,
I have seen some GeoTIFFs for DSMs (float32) with NaN as no-data value. It was not set in the metadata, but worked as that.
Most (I wouldn't claim "all") code in GDAL that does no-data checking does for floating point values "if (std::isnan(pixel_val) || pixel_val == nodata)", so yes, even when not advertized as the band nodata value, a NaN pixel will be deal as it
 I think I have also seen it with NaN set in the metadata.
Also many other numbers as no-data value, like -10000 or -9999 or -8888 (yes, and many other posible values).

Is there any reason to prefer or discourage NaN as a no-data value for a float32 GeoTIFF?

If you are curious there is a 10 page essay on that topic on https://docs.ogc.org/per/24-040r1.html#Geomatys_contribution_misconceptions_about_NaN . Personnally that didn't help me to draw a conclusion on your question. Maybe except that both suck in different ways.

Even

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