No. I don't think so.
There is QE going on in the US. And the Americans are not buying coins like there is no tomorrow.
So i dont think the EU will either.
The two situations are quite different. The reason QE in the US hasn't led to rampant inflation/rush into commodities is because they've kept commercial interest rates low but the fed has singularly offered a favourable interest on excess reserves to banks.
This policy has arrested all the new money and pulled it back onto the fed balance sheets, so although the theoretical money supply has massively increased, it hasn't found its way into the economy. This policy has been successful so far in preventing a "Weimar" situation, but a couple of things could change all that:
[1] - a new round of wage growth which puts pressure on interest base rates to go up again
[2] - a currency war - e.g. with the Rouble or the Remnimbi
Europe, on the hand has been suffering from the opposite problem - deflation. Relaxed monetary policy by the ECB has suffered from a lack of "transmission" into the real economy. (To me and you that means that people are sick of debt and so haven't been borrowing. If they're not borrowing then no new money can be created and the economy suffers from a liquidity drain). There just isn't enough money around for the economy to grow. It's no use central banks printing money if the commercial banks can't "lever" that new capital via the fraction al reserve system.
In conclusion, I think a round of QE be the ECB won't have any net effect on Bitcoin, but will be symptomatic of the last 5 years of policy having failed to achieve growth. It might be seen as the ECB "throwing in the towel" and not knowing what to do next. It will probably boost the stock market in the short term cos there's nowhere else for the money to go.
All of this will be a precursor to major economic revaluation which could then see Bitcoin start coming to the fore as one of the "new economy" target commodities.