Yes, if your EFC is not actually a practical number in terms of - "Okay, this is what I'll have to write a check for." Your school just uses it to determine what kind of actual aid you will qualify for. They usually make "packaging groups" based on various factors - EFC, year in college, date of application. Various packaging groups qualify for various Depending on how expensive your school is, how many scholarships you have, what kind of funding the school has, and how they've decided to divvy-up their campus based grants, you may end up being responsible for more than your EFC, or less. It's just not something you can look at and think about in practical terms, and I wish that the FAFSA were clearer about that. Your EFC can be much lower than the cost of attendance at a particular school, but not low enough for grants - and you might still have to finance the whole thing with loans in an amount even higher than your EFC.
If you go to a private school, the lines may be more blurry, because they may have their own private grants, even if your EFC is not low enough for federal grants. It cannot hurt to have your FAFSA sent to any school your child might really want to go to (though you'll probably have to apply for admission to see an aid package). You never know what your aid will look like until you've applied.