Brown has had a good noggin scratch over this one.
The most significant abnormality in her vital signs is her profound hypoxaemia. If she has diffuse rhonchi when you listen to her lungs, then there is obviously some sort of mechanical obstruction to gas exchange such as foreign material (for example, vomit) or fluid (for example, blood or pulmonary oedema fluid). I use the term mechanical to differentiate it from a biochemical cause; for example, monoxyhaemoglobin binding or something of that nature. In this case, in theory, I suspect there will lbe no clinically significant difference between good basic oxygenation and ventilation with, for example, an LMA and intubation.. Certainly, an endotracheal tube has less leak than, for example, an ventilation with a bag and mask or LMA, but I dno not think the amount will be clinically significant. The same analogy applies as to say giving 100% oxygen does not increase oxygen delivery to an ischaemic myocardium because it cannot pass the occluded artery. If there is something interfering with gas exchange then changing from something else to an endotracheal tube will not fix that problem.
As to your question .... it surprises me nobody has looked at the facts overall. The most obvious being: how far away is the hospital and can it do what this lady needs? If a hospital that can secure her airway, do at least basic investigations to see what might be going on, and provide basic intensive care (ventilation at least) is close by (less than say, 20 minutes by road), then personally, I would just keep up basic airway manoeuvers and take her to hospital. If the hospital is far away, or the local hospital cannot do these things, then it is more sensible to look at securing her airway more definitively on scene.
You raise an interesting proposition of just giving her a general anaesthetic and making her unconscious without neuromuscular blockade. I accept that in many operating theatres around the world every hour of every day, many patients are simply made unconscious and have their airway looked after, perhaps including with an endotracheal tube, without neuromuscular blockade. This may even be clinically suitable for some patients seen by ambos. I must, however, question the logic in doing that. If you are going to do something, do it bloody properly. I do not see the point of doing things by half measures. particularly in the "general" type of patients seen by ambulance personnel who tend to be more unwell than your average person requiring elective general anaesthesia. I am sure I do not need to state the obvious disadvantages of laryngoscopy for intubation, particularly on someone with a traumatic brain injury, without neurmuscular blockade. Whatever medicine of flavour you can choose I suppose .... although I do not see a great benefit in simply using suxamethonium. I accept in most operating theatres, elective anaesthesia uses suxamethonium, but again, I think it common ground the type of patients seen by ambulance personnel are different enough that a long acting medicine (for example, rocuronium) is more preferable. That said, I accept there may be the odd patient who is actively dying and needs an airway immediately, more immediately than taking the time to set up for full sequence anaesthetic and intubation. The example I can think of is someone with rapidly worsening pharyngeal oedema or something. I suppose in that situation with a choice between quickly making them unconscious or being faced with an obstructed airway you cannot pass an endotracheal tube through, that is the exception. I have not obviously discussed the patient in cardiac arrest as that changes clinical priorities quite somewhat.
Hope that is as helpful for you as it was interesting for me.