With small kids--last I heard, and it's been a few years--their basic policy is that they'll help find doctors, therapies, etc. to minimize the likelihood of using blood. But the courts will always order blood if the doctor believes there's no other option, and the HLC tells the parents not to resist. Very different from the 70's, when they publicly praised a couple who went on the run with their sick toddler to avoid a court-ordered blood transfusion.
With adults, hospitals in the US now have standard bureaucratic processes for respecting patient treatment decisions, so it's usually not a big deal anymore. My witness father-in-law was in a car accident a couple of weeks ago, and the doctor tried to persuade my mother-in-law to accept blood for him, but when she refused, they went ahead and respected their wishes. The HLC didn't even have to show up; they just provided a form for my mother-in-law to fill out, indicating which fractions she would accept. (Luckily, my father-in-law pulled through without blood.)
I think the main area where there can still be problems is with older teenagers (e.g. the case of Bethany in Canada a couple of years ago). They're not old enough to have full rights to make their own decisions, but they're also old enough that the courts may respect their wishes. Those cases can be tricky.
P.S. Also, I know that at least some of the HIS staff (the Bethel group that manages the HLCs) doesn't even believe in the blood doctrine. Also, the Society is very focused on avoiding negative publicity or legal trouble. So the HLCs generally try to avoid controversy, and stay out of the way of medical treatment as much as they can without explicitly contradicting the holy GB.