Yes, it will die if the root ball dries out.
You should pot it up. The smaller the pot the better. You don't want a pot that will hold lots of soil, which will hold lots of extra water this young plant can not take up. If it is plug, a single stem tree about 12" tall more or less than try to find a 2.5-3" pot.
Keep it in the coolest room you have. Make sure you once a month wash of the needles with a spray mister or the sink mister. Spider mite are the biggest concern. Washing the plant once a month will keep any that take hold to a minimum population.
Then in spring you will slowly introduce it to a sunny location. Such as giving it one extra hour of direct sunlight a day. Spruce want to be planted in the sunniest location you can offer.
If you do not get much for rain, you will need to water it for the first few year. When you do water it, spray off the needles with water. I'm not sure your location, but where I live spider mite decimate young spruce.
The more care you give your young tree the better chance it will have to thrive.
Spruce also do not like wet feet. You want to plant it in a place with decent soil, that does not get water logged when it rains. or a low spot in the yard that collects rain. They require well draining soil.
Norway Spruce - Missouri Botanical - Plant information