No.
The original concept had the first 3 digits identifying a regional office that issued the number.
And no SSN has been issued with any group of digits having all 0's
Fore more info Wikipedia is good at this kind of stuff.
I read stories from older university alumni from back when SSN served as student IDs where someone who issued gym uniforms or something like that would wow students by telling them where they were born when they’d tell him their SSN.
I went to state college in the 90s and they posted test scores with SSNs. That is when I noticed that most of the students had one of two three digit prefixes. Thought it was based on when they were issued, looked up how SSNs worked and found out about the location pattern.
This was before the credit industry hijacked the number and started treating it as a secret code, despite SSNs not being intended for anything other than Social Security.
When I went to college early 2000's, my SSN was printed directly on my student ID card. It was the unique ID that the university used for each student. Then like a year or two later, they required all the students to get new IDs without the SSN printed on them.
No, originally the first three digits designated where you lived when you requested your SSN. The middle two were also not sequential. The final four digits were the only purely sequential ones.
Fun fact: whenever I'm in a 7-Eleven, I use whatever area code is for that area and then Jenny's number, and it always brings up an account for their rewards program and saves me some money. Thanks, Jenny!