Yes, of course the crew should know the condition of the casualty - as a SAR crew you are making a constantly updated risk assessment and there will always be some risk attached to any SAR mission.
How much risk you and your crew are prepared to take will depend in some circumstances on the condition of the casualty - do you let the casualty bleed out on the hill or do you accept the additional risk of hover taxiing in poor vis?
Some of your acceptance of risk will depend on your 'plan B' - in the case of the SAR video, they had an IF abort option if they did lose all visual references - the sort of thing the crews are trained for and are very well within their capabilities.
What is the point of having a super-modern helicopter with all the bells and whistles if you are not going to use it to its full capability because the weather is a bit bad?
Anyone who thinks you can make SAR super-safe with PC1 profiles all round and no-go weather limits is kidding themselves and better hope they are never the ones in trouble.
It is too easy to criticise the actions of the Italian HEMS crew from the comfort of ones armchair - anyone who has spent any time in the mountains knows that the weather can change very quickly and anyone can get caught out no matter how many safety protocols you have in place. The only safe way to operate is to not go flying in the first place but that doesn't help those in need.