Maybe in some very extreme case they would, but it is better that someone escapes custody than someone (including the suspect dying).
Then again, just a cop drawing a weapon or firing a weapon usually makes the news.
They won't arrest you the next chance they get (say, when your plate shows up on a scanner)?
I'd propose that avoiding jail indefinitely will eventually lead to violence in any halfway-organized jurisdiction. And if you start shooting, eventually the government will shoot back.
All over a driving misdemeanor. We just assume that reasonable people won't let these things escalate that far, but yes: Every law written is ultimately enforced by a man (or woman) with a gun.
Bottom line: If you are not a danger to anyone, they will let you escape rather than kill anyone (including you), even if it means you are never brought to justice.
It makes a lot of sense, if you don't have a revenge based justice system.