If by financial aid you mean Medicaid then yes it can. Most state will only allow $2000 or less in assets to qualify for Medicaid. If a life insurance policy has more than $1500 in cash value you will be required to dispose of the asset by either cashing it in and spending the money or irrevocably assigning the policy or cash value to a funeral trust or funeral home.
If you mean financial assistance for college, then the answer is generally no, in fact it would be encouraged so that there would be money available to pay off your student loans.
Term life insurance doesn't affect financial aid. Life insurance owned by a trust and out of the estate doesn't affect financial aid. However if the cash values of a personally owned life insurance policy are cited as an asset for personal bank loan purposes or business loans, it could be construed as a cash asset and may be characterized as an asset for financial aid means testing.
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If you mean financial assistance for college, then the answer is generally no, in fact it would be encouraged so that there would be money available to pay off your student loans.