No, dpkg -s just simply tells you if it is installed. If it's not then:
$ cd <directory where firmware-iwlwifi.deb
is then:
$ sudo dpkg -i firmware-iwlwifi.deb
or
# dpkg -i firmware-iwlwifi.deb
There should have been one installed by default. If it is installed then you can move onto the next step which would be configuring your network. That works exactly the same as any other desktop. Find the icon and click or right click and pick your network or adjust settings. I can't remember, it's been several years since I used a network manager.
Also for future reference, you may want to install the gdebi package or check your menu to see if it is installed. It will do the same thing as dpkg -i except it is a graphical program like you are used to and you will be able to install .deb packages from your file manager by clicking on them like you are used to using. I find such things to just simply get in my way but to each their own.