Yes. A thorough comparison of the gospels shows that "kingdom of heaven" is Matthew's term for "kingdom of God". Whenever "kingdom of God" appears in a parallel passage, Matthew almost always rephrases it "kingdom of heaven". I've highlighted these two phrases in the following examples.
The parable of the mustard seed
He also said, "With what can we compare the kingdom of God, or what parable will we use for it? It is like a mustard seed, which, when sown upon the ground, is the smallest of all the seeds on earth; yet when it is sown it grows up and becomes the greatest of all shrubs, and puts forth large branches, so that the birds of the air can make nests in its shade."
He said therefore, "What is the kingdom of God like? And to what should I compare it? 19 It is like a mustard seed that someone took and sowed in the garden; it grew and became a tree, and the birds of the air made nests in its branches."
He put before them another parable: "The kingdom of heaven is like a mustard seed that someone took and sowed in his field; it is the smallest of all the seeds, but when it has grown it is the greatest of shrubs and becomes a tree, so that the birds of the air come and make nests in its branches."
Little children and the kingdom
But when Jesus saw this, he was indignant and said to them, "Let the little children come to me; do not stop them; for it is to such as these that the kingdom of God belongs. Truly I tell you, whoever does not receive the kingdom of God as a little child will never enter it."
But Jesus called for them and said, "Let the little children come to me, and do not stop them; for it is to such as these that the kingdom of God belongs. Truly I tell you, whoever does not receive the kingdom of God as a little child will never enter it."
He called a child, whom he put among them, and said, "Truly I tell you, unless you change and become like children, you will never enter the kingdom of heaven. Whoever becomes humble like this child is the greatest in the kingdom of heaven.
Sending the twelve
Then Jesus called the twelve together and gave them power and authority over all demons and to cure diseases, and he sent them out to proclaim the kingdom of God and to heal. He said to them, "Take nothing for your journey, no staff, nor bag, nor bread, nor money—not even an extra tunic.
These twelve Jesus sent out with the following instructions: "Go nowhere among the Gentiles, and enter no town of the Samaritans, but go rather to the lost sheep of the house of Israel. As you go, proclaim the good news, "The kingdom of heaven has come near.' Cure the sick, raise the dead, cleanse the lepers, cast out demons. You received without payment; give without payment.
Altogether, the phrase "kingdom of God" appears 52 times in the gospels (31 times in Luke, 14 in Mark, 5 in Matthew, 2 in John). The phrase "kingdom of heaven" appears 31 times in Matthew—and nowhere else. There is no reason not to think it is meant to be synonymous with "kingdom of God".
There are a number of other examples in the synoptic gospels where one or more writers choose a synonym rather than sticking with the original word. Here are a few examples.
The transfiguration—Peter's words
Then Peter said to Jesus, "Rabbi, it is good for us to be here;
Then Peter said to Jesus, "Lord, it is good for us to be here;
Just as they were leaving him, Peter said to Jesus, "Master, it is good for us to be here;
The transfiguration—God's reply
Then a cloud overshadowed them, and from the cloud there came a voice, "This is my Son, the Beloved; listen to him!"
While he was still speaking, suddenly a bright cloud overshadowed them, and from the cloud a voice said, "This is my Son, the Beloved; with him I am well pleased; listen to him!"
Then from the cloud came a voice that said, "This is my Son, my Chosen; listen to him!"
The abomination of desoloation
But when you see the abomination of desolation standing where he ought not to be (let the reader understand), then let those who are in Judea flee to the mountains.
So when you see the abomination of desolation spoken of by the prophet Daniel, standing in the holy place (let the reader understand), then let those who are in Judea flee to the mountains.
But when you see Jerusalem surrounded by armies, then know that its desolation has come near. Then let those who are in Judea flee to the mountains…
These differences can sometimes provide clues to the identity of the author or of the original recipients of the gospels.