You are checking against what you promise the world to do, not what you actual do.

This will always add, which isn't what you want. You want something like:

int txSigCheck = nSigChecks.load();
while(txSigCHeck <= MAX_TX_SIGCHECKS_COUNT) {
    int newTxSigCheck = txSigCheck + metrics.nSigChecks;
    if (nSigChecks.compare_exchange_weak(txSigCheck, newTxSigCheck) {
        return newTxSigCheck <= MAX_TX_SIGCHECKS_COUNT;
    }
}

return false;

I'm not convinced this is the best place, especially since it could be opaque in this header.

If this the responsibility of the class to handle its innards, then why this? You'll note that this is simply communicating infos to the outside, because there are actually nothing enforcing that it is used in the inside. This does seems to be achieving anything.