In her capacity as Solicitor General prior to taking the bench, Justice Kagan provided the Supreme Court a letter in connection with New Process Steel in which she stated that "the Senate may act to foreclose [recess appointments] by declining to recess for more than two or three days at a time over a lengthy period" - pointing to pro forma sessions that the Democratic-controlled Senate employed in 2007 to block George W. Bush from making recess appointments (in particular, recess appointment of the then-chairman of the NLRB). It is certainly conceivable, but hard to imagine, that Justice Kagan would both fail to recuse herself and would abandon her prior public position.
Defenders of any sort of recess appointment power would have an uphill battle, in my opinion. Assuming the rest of the Justices remain aligned as they were in New Process Steel, the Executive branch would have to pull off a triple play of sorts: (1) getting Justice Kagan not to recuse herself, (2) persuading her to adopt a position at odds with her prior public position, and (3) persuading Justice Kennedy not to go with the rest of the conservatives. If Justice Kagan does recuse herself, and the Court splits 4-4, then the result in Noel Canning would stand as it is. So the odds seem to favor an affirmance.