I have to note, as with any SEO question, the answer is just my opinion and not knowing the full and specific scenario, take it with a grain of sale.
As a general rule in that scenario though I'd simply let the bots do what they will with it but make sure to canonical the page to itself so if the other sub you're CNAMEing gets picked up it canonical's back to the real one.
In essence, let the link weight flow as it will - just make sure you don't get hit with a dup-content issue on the page.
As for ranking ... I'd focus your energies on the main site unless there's a term that the page lends itself to. But then ... that's pretty much a global truth: focus on rankings a page with content that lends itself to the term you want to rank for.
Good luck !!!
Dave