You will be able to use the DLC online, but there are limitations.
Nintendo has detailed how the upcoming DLC will work in terms of online play for Mario Kart 8.
For online play, you can use both regular and DLC characters to play on the original 32 tracks, and those who don't have the DLC will be able to see the unlockable DLC characters in play. There will also be options for those who have the DLC to play with the eight new tracks online as well. However, if someone joins and they do not have the DLC, the option to use the eight additional tracks will disappear. Only those who have the DLC will be able to use the tracks online.
The first batch of Mario Kart 8 DLC will be released on November 13 for $7.99. The second DLC pack will be released this May.