I've been administrating an office network that was set up by someone else and I always found this weird about it:
Their internal subnet is in this range: 172.253.16.0/24. It's been working fine, but it does not conform with RFC 1918.
I've been trying to find out who has IPs in the range 172.32.0.0/8, but a simple WHOIS only shows that they "belong" to ARIN. Could it be that they're simply unassigned? I tried ICMP pinging a wide range of them and got no response...
I guess I'll eventually change the subnet to something more standard, but it's a curious thing, don't you think?
No, it's not a valid private subnet, as you can seen in the RFC. You've most likely not had issues because of the use of NAT when hitting the Internet. In which case, you would only run into issues if you were trying to access something using that range.
You should take the time to correct the subnet to avoid any future problems.
Someday ARIN may allocate 172.253.x.y to somebody.
There are two sides to it, it will take effort to migrate away from your current configuration, and how likely is it that you will want to connect to that somebody.
But on the other hand, it will be a pain to troubleshoot, and resolve on short notice if you do want to connect.
The subnet does not appear to be assigned (yet), but is not reserved for private use, as you already pointed out. You may want to switch it sometime soon before the address' are allocated.