To answer your question directly: Yes. You described it correctly.
However, I am addressing primarily the statement: and I would like to use my own DNS servers
You have a problem that may not have occurred to you yet.
Now for the problem:
You do not want to host your own domain name on your own NS servers that are sub-domains or your parent domain. You should never host your domain name on a network that requires your domain name to resolve. What happens if there is a problem?? It is impossible to fix a problem where your domain name is not resolving when they are on NS servers that require your domain name to reach.
I used to be a web host in my previous life. Yes. I did have my domain name in my DNS servers which were the SOA (statement of authority) for the domain name as much as the DNS servers knew, however I had two redundant high availability DNS servers on two other networks and I pointed the registrar to these. These external DNS servers pulled from my masters. The reason is simple. If anything were to go wrong with my network, it did not interfere with resolving my domain name(s). Hosting your own domain name on a network that requires your domain name to work, will spell disaster for you at some point likely sooner than later and it is nearly impossible to fix without being an expert and a long wait time.
I highly advise against what you are trying to do.
Your recovery time will be long.