DDNS Update Over-writes DHCP Registered address?

All,

Secure and Non Secure Updates are allowed through DDNS

A Client gets a DHCP Address
The DHCP Server is configured to do a DNS Update on its behalf...so it
does and it succeeds.
Client then has a DHCP Address and a registration in DNS.

The Client subsequently trys to update the DDNS Registration for its
record isself via an UN-SECURED update.

My question is...would it succeed?

The origional DDNS Update was done by the DHCP Server and should
belong to the DHCP Server...the following un-secured update should
fail...becuase the owner of the record is the only one who can update
it....right?

Cliff.