Conjured animals would gain temporary hit points
The Bear Spirit option of the Shepherd Druid's Spirit Totem feature states (XGtE, p. 23):
The bear spirit grants you and your allies its might and endurance. Each creature of your choice in the aura when the spirit appears gains temporary hit points equal to 5 + your druid level. In addition, you and your allies gain advantage on Strength checks and Strength saving throws while in the aura.
There is no limit to the number of allies this may affect; they simply need to be within the aura (a 30-foor radius).
There already exists the question "Does a familiar count as an ally?", and the most upvoted answer there states that yes, it does count as an ally. Note that "ally" is not a defined game term, so it comes down to its standard English usage; I would certainly call animals made by conjure animals allies, especially since the spell states:
[...] The summoned creatures are friendly to you and your companions [...]
Though this combo is strong, effects at that level may still kill the boars. For example, a fireball spell dealing 8d6 (28) fire damage would kill the boars, with or without the temporary hit points (on average).
For some math (from AnyDice), the odds of rolling an 11+ on 8d6 is nearly 100%; the odds of rolling 21+ is still a 93.93% chance. However, if they pass the saving throw, then you need to roll 22+ normally, a 90.93% chance, and a 42+ with the THP, a mere 0.18% chance.
Also, conjure animals is a concentration spell, so if the conjured creatures become a challenge for the enemy, they have a pretty good reason to now target you.