That's precisely the case as far as I can determine. As fed assets rise, reserve account balances also rise, rates fall, the dollar falls and the equity market typically rises. However, if demand is down, there may be, at the same time, little or no price inflation other than in the equities market. (When we say "inflation" we mean generalized price inflation,) unless we qualify the term. So during QE, equities may be better correlated with the dollar than with "inflation." Or said another way, a falling dollar does not always produce generalized price inflation.
Venezuela hyperinflation... 1,000,000-bolivar bills worth 0.53USD... USD in demand https://www.msn.com/en-us/money/mar...la-to-print-1000000-bolivar-bills/ar-BB1ei8Dj https://www.bloomberg.com/quote/IBVC:IND