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I haven't tried it but imagine it would work. However in interviews i've seen with Rob, he states that the Hero Realms cards do more damage and heal for more, making Star Realms weaker. Hero Realms also has more bases/champions further making star realms cards weaker.
Pit one against the other Star Realms is weaker
Mix them up and Star Realms cards cost more for value.
Both sets would be weaker actually, as cards that care for champions wouldn't see bases, and vice-versa, while card sthat care for ships wouldn't see actions, and vice-versa.
The ally abilities also wouldn't trigger, as the symbols differ from Star Realms to Hero Realms.
This would be easier to fix as house-rules, but since the factions' roles have been swapped, the game would feel less cohesive : yellow in Hero Realms does what blue did in Star Realms, for instance. That might be an interesting synergy though, gaining life and stunning champions as an ally ability.
As mentioned above, though, cards in Hero Realms are costed way more aggressively than in Star Realms. The almighty cutter would suddenly become a terrible card