You are correct. The Union would only have to wait a year after the conduct of the prior election before petitioning for a new election. Obviously, a year has now gone by so if the players rejected the Union, the Union could file a new petition seeking an election among the current bargaining unit players. MRCat 95 is also correct that the Union at any time could seek to organize teams at other private schools.
Other schools would probably not agree to conduct an election based on the Northwestern decision and would go to a hearing contending that somehow the facts that established NU players to be employees do not exist at their programs. Faced with a new election petition even NU might force the matter to another hearing contending that the facts have changed since the first hearing. Nevertheless this time the process would be quite a bit faster. The Board doesn't have to grant Review of Regional Directors' Decisions. If the Board doesn't see any substantial reason why its decision in our case isn't controlling, it won't grant review of the Regional Director's Direction of Election in future cases and will simply summarily adopt the Director's Decisions in those cases directing an election.
I don't believe that the Union will necessarily file another petition at NU if it loses the election. First, it can't even file a petition unless it can demonstrate support from more than 30 percent of the bargaining unit. Second, Union's don't like to file petitions and lose elections. Campaigns are time consuming and expensive. They have a lot less money to spend on these campaigns than Employers. Most Union's won't file petitions unless they initially have the support of well over 30 percent of potential voters. I guess what I am saying is that I don't think the Union will file another petition unless they believe they have a realistic chance at winning the second time around.