I don't think so. If you have a shard of a particular type I think there is a chance he will get that trait when leveling up

I am looking at the code for Air1 vs Air2. It seems that Air1 has no tag for probability while Air2 is rated as common. Hard to say what the deal is here. 

<AbilityBonus InternalName="Air1Ability">
<AbilityBonusType>Champion_Spellbook</AbilityBonusType>
<AbilityBonusType>Unit_Spell_Rank</AbilityBonusType>
<SpellbookType>Air</SpellbookType>
<AbilityBonusOption InternalName="Air1">
<DisplayName>Air Apprentice</DisplayName>
<Description>Allows the unit to cast rank 1 Air spells like Evade and Haste</Description>
<Icon>Ability_AirApprentice_Icon.png</Icon>
<GameModifier>
<ModType>Unit</ModType>
<Provides>Allows the unit to cast rank 1 Air spells like Evade and Haste</Provides>
</GameModifier>
<Cost>1</Cost>
<IsCombatAbility>1</IsCombatAbility>
<SpellbookRank>1</SpellbookRank>
<AIData AIPersonality="AI_General">
<AIPriority>5</AIPriority>
</AIData>
</AbilityBonusOption>
</AbilityBonus>
<AbilityBonus InternalName="Air2Ability">
<AbilityBonusType>Champion_Spellbook</AbilityBonusType>
<AbilityBonusType>Unit_Level</AbilityBonusType>
<AbilityBonusType>Unit_Spell_Rank</AbilityBonusType>
<SpellbookType>Air</SpellbookType>
<AbilityBonusOption InternalName="Air2">
<DisplayName>Air Disciple</DisplayName>
<Description>Allows the unit to cast rank 2 Air spells like Aura of Grace and Guardian Wind</Description>
<Icon>Ability_AirDisciple_Icon.png</Icon>
<GameModifier>
<ModType>Unit</ModType>
<Provides>Allows the unit to cast rank 2 Air spells like Aura of Grace and Guardian Wind</Provides>
</GameModifier>
<Cost>1</Cost>
<IsCombatAbility>1</IsCombatAbility>
<Likelihood>450</Likelihood>
<RarityDisplay>Common</RarityDisplay>
<SpellbookRank>2</SpellbookRank>
<Prereq>
<Type>UnitStat</Type>
<Attribute>UnitStat_Level</Attribute>
<Value>3</Value>
</Prereq>
<Prereq>
<Type>AbilityBonusOption</Type>
<Target>Unit</Target>
<Attribute>Air1</Attribute>
</Prereq>
<AIData AIPersonality="AI_General">
<AIPriority>5</AIPriority>
</AIData>
</AbilityBonusOption>
</AbilityBonus>

I actually think that having Champions that are better for some stuff and not for other is quite good. If every Champion can end being "Master of the Five Elements", it doesn't sound so cool. I suppose it's a matter of preferences.

I think that the bonuses that you can get after choosing a Path are nice and in some cases really interesting (I'm in love with Tactician and Leadership) but it's true that they are not awesome as the Path traits... which is good or Champions would be totally out of control.

Currently, a champion with no spell traits can gain spells:

There is a spell that can be cast on champions to unlock a spell for that champion. They are named differently, but there are these spell-spells for Heal, Fireball, Drain Life, Shockwave. Unlocking these spell-spells (I don't have a better phrase, fuck you) comes from techs.

Check out the in-game hiergammemon on Annointed By Fire for example

I'm currently taking this personally.

It's only a handful of spells though, and they're limited in how often they can be cast, so it's still not a great solution to developing a hero with path of the mage, no spells, and the evoker trait (hah).

Should either guarantee a spell school once path of the mage is chosen, or not allow it to be taken if the champion has no spell schools.

In addition to those spells that are from the schools, a character that is imbued may also cast any spell that does not belong to any school. Again, these are mostly researched, but some are found.

I will post a full list, based on the XML in 0.75 beta. I will put it in spoiler tags to not spoil any surprise for anyone that does not wish to see it

edit: spoiler tag didn't work. I posted them off-site. Beware of spoilers. These spells may only be for campaign, I don't know. Again, spoilers.

http://pastebin.com/raw.php?i=Kh0XYU8K

The bottom line is this. Path of the mage may not be the best option for someone missing spell traits, but it is far from useless.