The Center for Retirement Research at Boston College has issued a report asking "Does the Social Security 'Statement' Add Value"? The Social Security "Statement" they're talking about is what the agency calls the Personal Earnings and Benefit Estimate Statement (PEBES).
Most people say they remember receiving PEBES and found the information helpful. However, there is little evidence that PEBES affects claiming behavior and there's little evidence that people remember the amount they will receive when they retire. See the chart below.
For what it's worth, my clients often ask how much they'll receive a month if their disability claim is approved. I seldom have easy access to this information until close to the hearing. When I'm asked this question, I ask the client if they remember receiving the PEBES -- describing it in a way such that they'll understand what I'm talking about. They generally remember receiving it and say they have saved it. I tell them that the PEBES tells the approximate amount that their disability benefit will be. They're always surprised to hear this.