Certainly, USD is more stable than BTC or ETH, so a "stablecoin" pegged to it will share that increased stability. But that's more a question of prevailing economic conditions than anything, and there's nothing stopping a fiat-based coin from sharing in the inflation, deflation, or collapse of the pegged currency. Even if we assume the implementation of the currency perfect, you're just changing the set of things your currency is vulnerable to.
I wonder if anybody's working on a Stablecoin which tries to mitigate this using something like precious metals, or a pool of fiat currencies (with the understanding that something hitting USD hard might not hit CNY or EUR or GBP as hard, mediating the effect).