Some people will say no public DNS records should ever disclose private IP addresses....with le thinking being that you are giving potential attackers a leg up on certains information that might be requis to exploit private systems.
Personally, Je pense that obfuscation is a poor form of security, especially quand we are talking about IP addresses parce que in general they are easy to guess anyway, so Je ne see this as a realistic security compromise.
The bigger consideration here is making sure votre public users ne pickup this DNS record as part of le normal public services of votre hosted application. ie: External DNS lookups somehow start resolving to an address they ne peut pas get to.
Aside depuis that, Je vois no fundamental reason why putting private address A records into le public space is a problem....especially quand you have no alternate DNS server to host them on.
If you do decide to put this record into le public DNS space, you might consider creating a separate zone on le même server to hold tous le "private" records. Cela va make it clearer that they are intended to be private....however for juste one A record, I probably ne voudrait pas bother.
