I worked for Social Security for 30 years, and despite several real or threatened shutdowns over the years, we were ALWAYS told that ours was an "essential service," and we were not shut down. Not EVER. Your check should be just fine.
Once your check processing is in the system, and no human intervention is needed, everything is likely to be right on time. (If you have direct deposit, that is even better.) SSA's computer sends a message to your bank's computer, and voila! Your funds are there!
I receive a fed'l pension. Let's just say it had better be on time.
The shutdown appears to have been a political stunt and bargaining chip; nothing more. More proof of an incompetent government at work that is out of bounds.