Most likely not. Social security is not taxable unless the recipient has other income. If they have other income, the total other income plus 1/2 of social security would need to exceed 25,000 dollars before any social security income would be taxable
See IRS Survivor Benefits for a full explanation:
Question: Are social security survivor benefits for children considered taxable income?
Yes, under certain circumstances, although a child generally won't receive enough additional income to make the child's social security benefits taxable.
The taxability of benefits must be determined using the income of the person entitled to receive the benefits.
If you and your child both receive benefits, you should calculate the taxability of your benefits separately from the taxability of your child's benefits.
The amount of income tax that your child must pay on that part of the benefits that belongs to your child depends on the child's total amount of income and benefits for the taxable year.
To find our whether any of the child's benefits may be taxable, compare the base amount for the child’s filing status with the total of:
One-half of the child's benefits; plus
All of the child's other income, including tax-exempt interest.
If the child is single, the base amount for the child's filing status is $25,000. If the child is married, see Publication 915 , Social Security and Equivalent Railroad Retirement Benefits, for the applicable base amount and the other rules that apply to married individuals receiving social security benefits.
If the total of (1) one half of the child's social security benefits and (2) all the child's other income is greater than the base amount that applies to the child's filing status, part of the child's social security benefits may be taxable. You can figure the taxable amount of the benefits on a worksheet in the Instructions for Form 1040 , Instructions for Form 1040A , or in Publication 915 .