Isn't that what FRS had been doing during QEs? The newly printed money went directly to financial markets, them hitting new highs. Did it contribute to the devaluation of the US dollar? If it did, then why is the USD index soaring? I guess in today's perverted world with the currency wars raging, it is not so straightforward as it had been in the good old days...
It might have a lag effect. Which is why the US is so concerned about inflation and ended QE.
Interest rates are going to go up some time this year too. This is a pre-emptive measure to prevent high inflation.