If an airfield has an ICAO locator, does this mean that PPR is not required under the convention agreements?
The two items are mutually exclusive and nothing to do with each other.
ICAO addresses are purely signals addresses - nothing to do with whether the operator wants PPR or not. The only part of the address actually agreed by ICAO is the first two letters - the remaining two are issued nationally for connectivity or a link to the AFTN.