No, it doesn’t.
The price to level up a kingdom are as such:
level 2: 500 gold
level 3: 1 000 gold
level 4: 2 000 gold
level 5: 4 000 gold
level 6: 8 000 gold
level 7: 15 000 gold
level 8: 22 000 gold
level 9: 30 000 gold
level 10: 40 000 gold