Let's take the BitUSD example. For every BitUSd that is created twice the amount uf USD in BTSX has be put up as collateral and you have to buy into BTSX with BTC and or USD.
The money supply of BitUSD depends on the demand for it. The money supply of BTSX is basically fixed. And the money supply of the USD does not corrolate with anything BitAssets do.
Derivates also do not inflate their underlying. But a derivates also normaly is not used in the same way as the underlying like it is with BitUSd and USD. So we could say that in addition to the USD an USD equivalent comes into existence which inflates the "functional category USD".
The market cap of BitTC would not depend on the amount of BTC (21m) but on the demand and value of an asset which is pegged to BTC but has the properties of BTSX.
BitUSD is not a derivative because there are no contracts. The same value exists in any form and BitAssets simulate and map value through the pegging process. BitUSD is just a label which represents USD buying power. It doesn't inflate the USD any more than bartering with baseball cards would.
But it does help the US economy because BitUSD can purchase USD. That purchased USD is the real USD.
In the case if BitBTC if you had too many (far beyond the cap) then they would still hold value but would they peg? I would think yes. If the market cap big enough to peg that many BitBTC then demand for BitBTC would surpass the demand for the original BTC.
BitBTC could basically replace the original BTC but would have similar characteristics of the original. A better question is what happens if BitBTC replaces BTC and BTC ceases to exist? Can we revoke BitBTC if there is nothing to peg it to?