Yes. The IRS will use the information on the Form SSA-1099 or Form RRB-1099 to generate Economic Impact Payments to recipients of benefits reflected in the Form SSA-1099 or Form RRB-1099 who are not required to file a tax return and did not file a return for 2018 or 2019. This includes senior citizens, Social Security recipients and railroad retirees who are not otherwise required to file a tax return.
Since the IRS would not have information regarding any dependents for these people, each person would receive $1,200 per person, without the additional amount for any dependents at this time.
You do not have to file a simple tax return to receive your stimulus check.
Below is an extract from this IRS document:
Economic Impact Payments: What you need to know
Updated April 1, 2020
The distribution of economic impact payments will begin in the next three weeks and will be distributed automatically, with no action required for most people. Social Security beneficiaries who are not typically required to file tax returns will not need to file to receive a payment. Instead, payments will be automatically deposited into their bank accounts. However, some taxpayers who typically do not file returns will need to submit a simple tax return to receive the stimulus payment. When more specific details become available, we will update the coronavirus page.