Personally, I believe so, as emotions are hormone driven. The different hormones evolved for different reasons. For example, cortisol is the negative response hormone (the one responsible for the pain of loosing a friend, for example) and is present in reptiles. Reptiles in general do not bond. Very few care for their young in any way, and many actively cannibalize them. Cortisol is part of an evolutionary process by which harmful and potentially harmful things are avoid through negative responses.
On the other end of things, the bonding hormone oxytocin allows us to form mating unions to breed and rear young, and well as encourage community, which in many species makes survival easier.
Well, if we look at things from the perspective of a theoretical brain-engineer trying to design a mind, it seems to me that emotions stand out as having immediate utility.
Specifically, that they're very logically simple. Emotional criteria to physiological response have a 1:1 mapping, little need to think about things and no need to have any logical capabilities like humans have.
So I'd say that emotions probably substantially predate intellectual capabilities like logic and language because that's primarily what a brain does without them - process input and convert it into general emotions that have set responses. (this also seems to address the question 'do animals have emotions')
This explanation is independent of the existence of evolution but makes more sense when evolution is a thing, because it's clearly a legacy measure from earlier development and a theoretical divine designer has little need for an iterative design approach..