Will it? We can only speculate what will happen in euroland as we have never had QE before for the euro.
But e.g., in the US QE has tailed off since 2014. Interest rates have risen since 2016 to 2.5%. Inflation increased in 2018 and then declined to 1.9%. In that period GDP has risen 3.4% and employment has fallen to 3.8%. https://tradingeconomics.com/united-states/indicators. So no carnage there.
In the UK QE has tailed off since 2018. Inflation rose and then declined to 1.0% Interest rates rose and then declined to 1.9%. In that period while GDP growth has declined, unemployment has fallen from 7% to 3.9%. https://tradingeconomics.com/united-kingdom/indicators. So no carnage there either.
It would appear that modest increases in interest rates after QE, i.e. that keep inflation at or below the target 2% rate, have not caused carnage. The USA has never had it so good, and considering Brexit-related uncertainty, the UK hasn't done too badly either.