Hi @Andres Del Rio,
Welcome to Microsoft Q&A Platform. Thank you for reaching out & hope you are doing well.
Yes, your understanding is correct.
The way the flows would work, traffic towards the DB would not go through the NAT gateway, as on the DB connection string you are pointing directly to the private IP of the DB (10.1.2.5) which is configured on Private mode linked to that subnet.
Hope this clarifies!
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Thanks,
Sai.