Technically speaking, “no” God does not have emotions. Emotions are a result of changeableness. God is one eternal divine act, which in His very nature is the self-emptying love between the Three Persons of the Most Holy Trinity.
I therefore view the language of scripture attributing “emotions” to God as figurative, for the benefit of human beings, rather than testament to the actual reality of God.
We must always respect the transcendence of God.
Yes, the Son of God assumed a human nature, however the divine and human natures in Him do not “mix”. He is WHOLLY GOD and WHOLLY MAN. It is Christ in His Human Nature and human soul who experienced emotions. Not in His Divine Nature!
God does not experience sorrow or pain according to the Fathers and scholastics. He cannot “suffer”, that is part of what the doctrine of impassibility entails:
***Saint Thomas Aquinas: Summa Contra Gentiles I.LXXXIX.12 ***
“…Sorrow or pain, for its subject is the already present evil, just as the object of joy is the good present and possessed. Sorrow and pain, therefore, of their very nature cannot be found in God…God cannot repent (change His mind) or be angry or sorrowful…”
St. Pope Gregory the Great also tells us:
Pope St. Gregory the Great (c. 540 - 604)
God is called jealous, angered, repentant, merciful, and foreknowing. These simply mean that, because He guards the chastity of every soul, He can, in human fashion, be called jealous, although He is not subject to any mental torment. Because He moves against faults, He is said to be angered, although He is moved by no disturbance of equanimity. And because He that is immutable changes what He willed, He is said to repent, although what changes is a thing and not His counsel.
(Moral Teachings From Job, 20, 32, 63; in JUR-3, 317)
The witness of some two other Fathers on this issue:
St. Clement of Alexandria (c. 150 - c. 215)
Here again arise the cavillers, who say that joy and pain are passions of the soul: for they define joy as a rational elevation and exultation, as rejoicing on account of what is good; and pity as pain for one who suffers undeservedly; and that such affections are moods and passions of the soul. But we, as would appear, do not cease in such matters to understand the Scriptures carnally; and starting from our own affections, interpret the will of the impassible Deity similarly to our perturbations; and as we are capable of hearing; so, supposing the same to be the case with the Omnipotent, err impiously. For the Divine Being cannot be declared as it exists: but as we who are fettered in the flesh were able to listen, so the prophets spake to us; the Lord savingly accommodating Himself to the weakness of men.
Origen (c. 185 - c. 254)
“…When we read either in the Old Testament or in the New of the anger of God, we do not take such expressions literally, but seek in them a spiritual meaning, that we may think of God as He deserves to be thought of. And on these points, when expounding the verse in the second Psalm, ‘Then shall He speak to them in His anger, and trouble them in His fury,’ we showed, to the best of our poor ability, how such an expression ought to be understood…But as, in what follows, Celsus, not understanding that the language of Scripture regarding God is adapted to an anthropopathic point of view, ridicules those passages which speak of words of anger addressed to the ungodly, and of threatenings directed against sinners, we have to say that, as we ourselves, when talking with very young children, do not aim at exerting our own power of eloquence, but, adapting ourselves to the weakness of our charge, both say and do those things which may appear to us useful for the correction and improvement of the children as children, so the word of God appears to have dealt with the history, making the capacity of the hearers, and the benefit which they were to receive, the standard of the appropriateness of its announcements (regarding Him). And, generally, with regard to such a style of speaking about God, we find in the book of Deuteronomy the following: “The Lord thy God bare with your manners, as a man would bear with the manners of his son.” It is, as it were, assuming the manners of a man in order to secure the advantage of men that the Scripture makes use of such expressions; for it would not have been suitable to the condition of the multitude, that what God had to say to them should be spoken by Him in a manner more befitting the majesty of His own person. And yet he who is anxious to attain a true understanding of holy Scripture, will discover the spiritual truths which are spoken by it to those who are called “spiritual,” by comparing the meaning of what is addressed to those of weaker mind with what is announced to such as are of acuter understanding, both meanings being frequently found in the same passage by him who is capable of comprehending it.…”
There is thus a very clear patristic consensus here. They regarded any of the passages imputing emotion to God (anger, sadness, grief) as being analogous and metaphorical, for the benefit of mankind rather than a description of God’s very nature because they believed in impassibility.