Depends on what you have in your blood stream. If the tech takes a sample for medical tests, the prosecutor might just need a subpoena instead of a search warrant to find out what you've consumed.
This is true, but assuming you’re sober and there isn’t anything in your bloodstream that could be an issue, it’s still worth it, especially if you are older. People have had righteous shootings and then they keel over from a heart attack caused by the stress while the policeman is still looking around. Better safe than sorry.
And the police can’t really question you while the medic is working on you or transporting you to the hospital, allowing time for your attorney to catch up with you.