It is achievable in a discretised manner, but is not trivial and I certainly don't have time at the moment to give enough details, but you would need to combine a custom colourmap and use of a manual caxis setting.
e.g. you can make the very first element of the colourmap black. this is the value NaNs will take. However, if your colourmap is e.g. length 256 it is also the colour that the bottom 1/256 of the values will take, so if your data ranges up to 25600 then everything up to 100 would take this value.
That is the problem with trying to create such a specific colourmap. Your data gets mapped from whatever its range is onto the discretised 256 values of the colourmap so unless your data range is e.g. 1-256 it is hard to achieve exact colour cutoff points for an arbitrary data range.
You can create a colourmap of greater size so potentially that is an option, but it depends again on your data range. If it is e.g. 1 to 1000 then you can easily create a colourmap of size 1000 (or 1001 to include special NaN handling), but if your range is up to e.g. 10,000 then a colourmap of that size is rather infeasible and way beyond what the human eye can distinguish.
To separate the NaNs out you need to ensure that the lowest value in your data will map to the start of the 2nd bin in the colourmap. This may well require you to change your actual data to avoid having some of it fall into the first (NaN) bin.
