No, but there are finite number of traits to be chosen. (If you don't have a trait to pick the level up window will show up and you have the option to close it, but you wil still gain a level)

you also get +1 accuracy per level.

other traits that increase by level:

- acrobat (assassin/trained troops) gives +1 dodge per level

- calloused hide (some monster champions like Tuatha) gives +1 defense per level

- discipline (warrior tree / possible sovereign pick at creation / trained unit trait) gives an extra +1 spell resist & +1 accuracy/level

- hardy (sov trait) gives an extra +1 HP per level

- path of the defender gives an extra +1HP pre level

- mancer blood gives an extra +1 accuracy per level

- some spells/spell like abilites scale with caster level (for example flame dart or coal stones)

- there are a few items that scale with level (windhammer/baccos hammer/shocking longbow/ some of the "champion" plate armor items; maybe some others)