Nowhere in the documentation for ImportToolbox does it say to use arcpy.alias.toolname(). It says to use arcpy.toolname_alias(). Your syntax works, the syntax in the documentation does not, which is what led me here. Thanks for the tip, however you discovered it.
That explains it. I had to make the alias and the name identical to get it to work. Next time, I'll try it backwards from the documentation.
It works fine with spaces, if you're running into issues, post a code snippet and we can take a look. Here's an example of an import which works fine on my end:
arcpy.ImportToolbox(r'z:\pyt with spaces\more spaces.pyt')
# <module 'touche'>
