Yes, it seems quite possible. Although most of the brain of a large animal is dedicated to controlling its body, it seems likely that larger animals are likely to be more intelligent than smaller ones, on average
Evolution has more to work with: if you stumble across some useful polygenic combination related to neural development, then the extra brain volume can be a big force multiplier
Combined with their observed behavior, it seems likely they're quite conscious, self-aware, and emotional. One should be cautious to attribute human notions like "respect" - but maybe not. Maybe that's really what it is, like how their seeming mourning of deaths really may just be grief like the grief humans experience
Purely intuitively, I suspect they do have something like a feeling of camaraderie and empathy for fellow beings, and especially ones that seem to have complex behavior like humans. I'd be surprised if they can think something as rich as "are aware that we are intelligent like them" - but, who knows, maybe they really do have such thoughts but can't really outwardly communicate them.
Maybe a lot of animals have much more rational and complex inner worlds and internal monologues than we think but are just lacking the sufficiently sophisticated speech parts of the brain to really formalize it in symbols that other animals can interpret, with just a limited subset for communicating in a more broad and emotional way.
The exact nature of their intelligence and consciousness aside, they seem to be conscious and social enough that deliberately killing an adult elephant is within the same order of moral magnitude as deliberately killing an adult human, in my opinion.
