Possibly, possibly not. Consider the competition Unix had at the time it was released. A cut down version could've also made inroads into the desktop market (for business users).
If it would be priced at the same level of VMS or mainframe OSes, I am not sure.
Plus maybe the Xerox PARC attempts would been more successful if there weren't a cheaper UNIX workstation as alternative, in spite how they managed the whole process.
> "If it would be priced at the same level of VMS or mainframe OSes, I am not sure."
Why would it have needed to be priced that high? We're talking about software here, the cost of reproduction is close to zero. It could've competed in the same market space as CP/M.