Yes it can but make sure you understand your status and don't just assume that you can't get aid, you might well be able to.
What sort of convictions might affect the aid that I can receive?
Other than drug convictions, convictions for a forcible or non forcible sexual offense which are subject to an involuntary civil commitment upon completion of a period of incarceration for that offense your aid might be affected.
If I have been incarcerated for the said offense what aid can't I receive?
You will not be able to receive a Federal Pell Grant.
Can I regain eligibility for aid if I have had a drug related conviction?
You can regain eligibility and if you do regain eligibility during the award year you should notify your financial aid office immediately so you can get any aid that is due to you.
What if I have been incarcerated, will I be eligible for aid?
You can receive aid but it might be limited.
What happens after I have been released after a conviction?