Yes it is possible. Additionally, if you see an NPC you like but can't marry him/her, you can use a console command that changes their status.
I think this is the command:
Addfac <variable> 1
- Adds the selected NPC to a faction (e.g. addfac 19809 1
adds an NPC to the marriage-faction, allowing players to marry this NPC)
Note: Be very careful when using this command. If you use it on an important NPC it can break any quests related to that character.