This is one of those questions that gets into semantics/jargon/babblespeak.
The investigation completes, good or bad. The standard for completing the background investigation has to do with the report itself and not the nature of the information contained therein. That is, is all the necessary information there, have all the follow-up questions been answered, is the report properly formatted, etc etc etc.
For situations where the clearance requires the polygraph as well, it is just another datapoint. I’ve read on here where people can have an “inconclusive” poly and still be granted a clearance. In my experience (a couple inches wide but many years deep), the only similar situation I’ve encountered was when people who were already cleared and did not attain a “successful” poly were allowed to retain their clearance. Sometimes they didn’t even get asked to do another poly.
(I hope that last sentence makes sense, I tried to write it a couple different ways)
I don’t know if you’d be denied outright (and possibly entitled to appeal) or if it would be like you say, the ‘suitability’ rejection.