If you're talking about genetic inheritability, we run into a tricky situation. The spell's duration is "instantaneous," indicating that the spell's effect is permanent and not reliant upon continuing magical energy to remain in effect. In other words, the spell creates a permanent, non-magical change in the creature.
For that to happen to an animal, it would have to grow entirely new brain structures that somehow still fit inside its skull - we'll just assume that happens however it happens. However, now you're talking about an animal that has a radically different physiology than others of its species. If the physiological change is represented in its DNA (which would be necessary), and that change transmits to its gametes (unknown), then it may not be able to successfully mate anymore - or, if it could, the resulting brain structure in the offspring would be . . . troubling, to say the least.
Additionally, you'd also have to create enough awakened creatures to allow for the required genetic diversity the species needs to successfully propagate. That differs for each species, but you're probably looking at several dozen for most mammals. Also, you have to make sure they don't mate with ordinary members of their species, or else the trait would be watered down and likely lost over time since there would not be much selective pressure to maintain the trait.
So, long story short, if your DM rules that the DNA changes apply to the creature's gametes, then sure, so long as you awaken several dozen other members of its species and keep them isolated from ordinary, non-awakened members long enough to ensure their propagation - a process that could take decades, or centuries, or longer.