Note that if the above is the case, that would imply that the tracking error of your USD-pegged asset is correlated to the non-USD components of your numeraire. In a risk-off/flight-to-quality environment (depending on the exact circumstances, but in general) you'd expect EUR and CNH to drop in relation to the USD and often JPY to rise in relation to USD. The opposite would be expected in a risk-on scenario.
Presumably, your USD-pegged asset would drop in relation to the USD in a risk-off scenario and rise in a risk-on scenario, so in that case it would seem that your tracking error would tend to be correlated to the non-USD components of your numeraire basket. So, if macro risk-on/risk-off are the primary drivers of your pegged asset's tracking error, it would seem that your pegged asset would tend to have less volatility than USD if a GDP-weighted basket of major currencies is your unit of account.
Presumably, your USD-pegged asset would drop in relation to the USD in a risk-off scenario and rise in a risk-on scenario, so in that case it would seem that your tracking error would tend to be correlated to the non-USD components of your numeraire basket. So, if macro risk-on/risk-off are the primary drivers of your pegged asset's tracking error, it would seem that your pegged asset would tend to have less volatility than USD if a GDP-weighted basket of major currencies is your unit of account.