It will be hard to fully answer your question without knowing the history of the case, and without getting the details regarding the treatment method that was used (e.g. Time since the start of clinical signs till treatment, progression of clinical signs, using/not using supportive fluid therapy/blood transfusions, and so on).
I will try to provide you with some insight from my personal experiences with Babesiosis in cattle, hopefully, it will answer some of your questions.
The prognosis for babesiosis in cattle is determined by a few factors, and acute death even with initiating treatment is not something rare.
Based on the evaluation of three main parameters you will be able to achieve a more accurate prognosis:
Body temperature and other clinical signs (persistent high fever, or lower than normal, are connected with a more guarded prognosis, as well as hemoglobinuria/hematuria, ataxia, head pressing, etc.). PCV ( low values and progressive discoloration of plasma - strong yellow-orange to red color is an indication for terminal prognosis). Blood smears (parasites with defined morphology, and higher parasitemia values which increase over time, are also indications of terminal illness).
With all that in mind, you can get a rough estimation of the chances of success of your treatment.
Regarding the usage of Diminazene aceturate, for me, that is the drug of choice for the treatment of babesiosis in cattle. It's highly effective when given at the correct dosage and time - efficacy depends on timely detection early in the disease.
Alternatively, you can choose to use Imidocarb dipropionate, take note of the long withdrawal period needed before slaughter and milking, due to long-lasting residues in milk and meat.
As mentioned above clinical signs are also a key factor in determining the success rate of the treatment, and in the case of a recumbent animal, as you described, the situation is already poor.
As a side note, the same applies to the development of neurological signs (in the case of Babesia bovis), when seen, the chances of the animal surviving are really low.