I run into problem with this NODATA Handling while working with file that came from GDAL.
NoData within this float type file was set to -3,402823e+38. This value was also the statistic minimum and so it the image could not stretched correctly to visualize the real values in range -85 .... 140.
BTW IMAGINE registred the NODATA Value but its suggestion was "-3" while using "Set or Clear NoData Value".
A "Clear NoData" was impossible.
Pixel Data request delivered #########.### allways. So more or less a NAN-Value.
Finally I solved this with a small Spatial Model requesting all Values Lesser than -100 and setting them to 255 and define 255 as NoData.
Updating the statistics while ignoring 255 delivered acceptable statistic and possibility to stretch the image in the optimal way.
Probably also worthwhile reviewing this article and its comments if you want to know about "Setting NoData":