This is interesting. As far as I can see bitUSD is competing with the USD just as much as DOGE or EUROs. All these competing currencies lessen demand for each other. People who were holding USD sold it to buy bitUSD, or BTC or CNY or any other currency.
Therefore bitUSD is inflating the USD by lessening demand for it, the same as any currency. When a country stops accepting USD for oil that lessens demand for it in that country causing USD's to find their way back to the USA where they cause inflation. Hence the petrodollar being forced on people at the point of a gun (one of the first things the US did after invading Iraq was switch their oil back to USD from EUROs). That's why we don't here horrible things about Saudi Arabia (despotic regime) from the mainstream media, because they still price their oil in USD so we like them. So yes I would say it is inflating it, but no more than any other currency.
This is if we say that inflation is the weakening of a currency due to the demand vs unit ratio decreasing.
If you think about it, if half of the users of the USD suddenly died (lets hope not) and for some reason all the other users carried on using USD the supply would have effectively doubled without printing any more USD, resulting in inflation. So inflation isn't just about money creation but is about demand vs number of units.