It makes sense to me. If the pulse is increasing and the blood pressure is decreasing, you would expect outcomes to be worsening.
However, I think this can indicate a lot of things beside left ventricular failure. For instance, hypovolemic shock would result in a compensatory increase in heart rate, and perhaps a decrease in blood pressure if the system couldn't keep up with losses. So, I'm not sure the "shock index" will work for pre-hospital providers.
I'd be interested to hear from some people in hospital ICU/CC settings about whether or not this is used and what they think of it.