Will we be able to see anything during the Polar Night?

Yes! You can :)  Here is a link to an album containing photos taken during blue hour. 

The sun disappears from sight in mid November and gradually reappears in mid January. Due to the high mountains and fjords around Tromsø it takes some time for the sun to sneak past it. During this period the light becomes less and less. Around Christmas time it is the darkest it will get, though as you can see in the album that there is still enough light to go on a day tour and see things.

You can have a look here to see the sun set and set times for the year.