The topic of whether Notre Dame football is relevant or not is a door which swings in both directions. If we're talking about the amount of fans, media attention, money, opinion and tradition, then Notre Dame is as relevant as any program in the country.
It may be fair to say Notre Dame is not relevant anymore because the Irish haven't won at a consistently high level for 13 years, but the Irish program is hardly on its death bed and it is unwise to think that Notre Dame will never get back on the winning track.
To say that Notre Dame risks permanent irrelevancy if it does not join a conference is misinformed at best. What does Notre Dame gain in relevancy by joining the Big Ten?
If Notre Dame removes the things which make it unique (national schedule and fan base), what advantages will the Irish have in recruiting? Some may be lured by the promise of a conference title, but the same thing can be offered at Ohio State or Penn State. And guess what, there won't be all of the challenges outside of football at these other schools either.
Notre Dame will always be in the running for recruits who are looking for a great education to go along with football. But for those who are not as concerned with books, guess where they will be attending? It won't be Notre Dame, and joining the Big Ten only makes recruiting these difference makers that much more difficult.
What this relevancy argument really boils down to is winning football games and it has nothing to do with Notre Dame needing to join a conference.
The repercussions for Notre Dame joining the Big Ten are mostly negative and will not help the program win football games better than it can as an independent. A Notre Dame team that wins the Big Ten championship is as relevant as an independent Notre Dame team that makes it to a BCS bowl.
The mere application of a Big Ten schedule and possible conference championship does not make it easier or more difficult road to the BCS discussion. All it does is satisfy those who do not like Notre Dame's independence.
A 10-2 Michigan team will have a great shot at a Big Ten title and will play in a BCS bowl. A 10-2 Notre Dame team is just as relevant since they have proven they can and will go to BCS bowl games with that record.
What would bring about irrelevancy for Notre Dame is many more years of losing thus shrinking the programs fan base and profits. And although many a Notre Dame hater wants the world to believe that this irrelevancy is just around the corner (and only conference affiliation offers hope), the truth is that Notre Dame is a long, long way away from not being able to flourish and compete at the highest level as an independent program.