I think that the number of unicorns will be infinite, because if it were of course, then the new players could not create their unicorns.
I agree, will probably be like cryptokitties where the number is technically infinite, but some are more 'desirable' than others, or would be so common there would be little point in creating more of the same given there will probably be a transaction fee in using the ethereum network. The value would probably be higher for earlier generation unicorns, given they will be more rare or perhaps better in some other way.
Think of it a pyramid (funnily enough) with the most valuable early generation unicorns at the top, then everything else flowing down, with exceptions for super rare or interesting features having increased value.
Nice project, how to get rare unicorn?