Infected people are more likely to be symptomatic than not, as far as we know (for example from the Diamond Princess).

Even if it was only 10%, should I find reassuring that 6000 people (less than 2% of the population) would have to get infected for the collapse of the healthcare infrastructure to start?

29 ICU beds will not be able to handle the oncoming wave of patients. My city is roughly the same size population as Iceland and only has 900 hospital beds. I don't know how many of those are ICU, or could be converted to makeshift ICU as Italy has been doing.