A. Not likely.
If you open a HELOC but don't use it, it won't matter at all for FAFAA. If you actually take money out of HELOC but not using it (e.g. put into a bank account), it will increase your reportable assets and hurt your chance of getting financial aid.
In one scenario a HELOC might help, that is you have a sizable saving balance, it will be your assets and hurt the financial aid chance. You can use that asset to pay down mortgage, then open a HELOC for emergency use. This will help your chance of getting financial aid, but of course comes with risks if your home value decreases, you lose your job, etc.