Not really. QE is a swap. Bonds (or other financial assets) for cash. If I take a bond from you and give you cash, are you going to interpret it as a windfall and go on a spending spree?
Adding demand and thereby liquidity to a market creates a windfall that wouldn't have been there otherwise. Whether it's because you were sitting on a bond that was impossible to sell and now you have money because you sold it, or because you would have gotten $1000 for it and now you got $1200, that's a windfall.
Whether that money goes into buying groceries or buying other securities, I assume most of it will continue to circulate in the economy. If it doesn't, then it's pretty much a failure as a quantitative easing.
Central banks sit on bonds because they buy them as part of their open market operations, and they are legally required to make a market for treasuries so the government is funded.
