Garnet and Black Attack had an interesting roundtable discussion last week on whether fans of a particular SEC school should root for the conference as a whole. For example, should anyone but Commodore fans have pulled for Vandy against Virginia? Or non-Plainsmen gone for Auburn against Florida State?
Because I am a pedant, I must preface the rest of this. You should follow your emotion when rooting in sports, full stop. Your desires do not and will never impact the outcome of a sporting event unless you're some kind of wizard, and rooting for a particular team is inherently irrational. Sure, you get the most good feelings from rooting for a particular team, but I have seen and met enough fans to know that you could get the same thing from rooting for some other team. So, root for who your heart says to root for.
That then changes the question to whether it is good for your team to see other SEC teams do well. In the aggregate, the answer is an easy "yes".
There is a subjective element to how every NCAA postseason field comes about. The better the league's reputation is, the more likely it is that its teams will get into those fields ahead of other conferences' teams. It is especially important in the revenue sports, because more spots means more money to the conference, and the conference divides the loot evenly. The conference's good reputation has paid off concretely in football. The Big Ten didn't get it's desired national championship rematch in 2006, nor did the Big 12 in 2008, but the SEC did in 2011. Speaking of 2008, Florida skated into the BCS title game largely without controversy outside of the Texas and USC fan bases, and the size of its lead over the Trojans is kind of shocking given how good that team was that year.
Even if it is broadly true that conference strength is good for everyone, it might break down in the specifics. Take Missouri football, for instance. It is good for the team to have a strong West division carry the conference banner for a weaker and more winnable East division. It is good for those Tigers to see schools like Miami, Clemson and Florida State win games over its division rivals.
Those ACC teams being stronger hurts programs like Florida and Georgia because they will take recruits from them. Mizzou, meanwhile, doesn't go up against those ACC teams in recruiting all that often. Missouri fans, if they felt the need to align their emotional rooting interest with calculated logic, should have been rooting for FSU last January. A great program in Tallahassee is MU's best friend.
This line of thought also breaks down for teams that are not usually in playoff contention. Looking at history, a weaker SEC in football is better for the Mississippi schools or Vandy and Kentucky as it gives them a better shot at going to bowls. I'm not sure any single inter-conference game will make a difference to that end, though.
Overall, the best thing for your school would be for it to win conference and national championships nearly every year. Failing that, and that plan will fail, then you want to see an SEC that does well with a rotating cast of characters at the top. That way, the conference keeps its good name while allowing for your school to have its turn at or near the top. We have actually had that in football to a degree for a while. No team has won consecutive SEC football titles since Tennessee in 1997-98, and only once—Florida's run from 1993-96—has anyone attended more than two consecutive title games. We have not had that rotating parity in a while in men's basketball though, and recent success by the top duo of Kentucky and Florida has not been enough to keep the league's reputation afloat.
So in short, you should still root for whatever your heart tells you to. When you come down from the emotion of the game though, know that a stronger SEC is probably more positive than negative for your team.