Well the main problem is that the host/hostel staff have yet to meet you. They don't necessarily know you, and they don't know what emergency it will be for.
So the call might go something like:
Operator: What's your Emergency?
Host: Er, I'm not sure. Someone's meant to turn up, and they haven't?
Operator: Can you describe them?
Host: No, I've never met them.
And so on. At best, you could get them to report you as a 'missing person', but the timeframe for when police consider you to be really missing differs from country to country.
In Australia, for example, you don't need to wait 24 hours to declare them missing, IF you have serious concerns about their safety/wellbeing and their whereabouts are unknown. However, generally it's for cases where being missing is out of character, which is hard to say if the host doesn't know you.
In New Zealand, however, if you do a hike you can state when/where you are expected to be/return, and if you don't show up a rescue party can be sent out to find you.
So long story short - it depends. Based on this, the call could go:
Operator: What's your emergency?
Host: Bart Arondson, a guest of mine was meant to arrive today and hasn't. He was going to be hiking from Nelson to Pelorus Bay today, and left there this morning but hasn't arrived here.
At which point the police/search and rescue might make a judgement call about the weather, conditions and the likelihood that you're in trouble.