On the one hand, you say, “I personally think when applying ED it helps if you don’t apply for aid,” then under the same breath you also say, “we have to figure out whether it can be helpful or harmful to apply for FA.”
The bottom line is, if your student is qualified for admission, then it doesn’t matter whether you check off the box or not. Colleges are more interested in filling the class with well qualified students than those who can merely afford the full COA. Most students, after all, do need FA and they do check off that box. If – and that’s a big if – there’s any advantage at all for leaving the box blank, that advantage will not make up for any deficiency in the application itself unless you’re willing to chip in a cool $2 million or more as a donation in addition. The point is not to hinge your student’s chances on whether you check off that box or not. If your student qualifies, then your student qualifies. If not, that box isn’t going to determine that.