I would say no.
Revelation is of course notorious for the diversity of interpretations. But when it comes to interpreting particular words, there are probably two primary options: the word is literal or symbolic.
If we take these words with their normal literal meaning, then throne and altar are different objects. It is arguable that if the altar is "before the throne" and the martyrs' souls are "under the altar" then they are also "before the throne". But in that case why didn't John say "before the throne"?
It seems obvious to me that because throne and altar have different meanings, John is wanting to bring out those different meanings by referring to throne or altar in appropriate contexts. Which leads me to the symbolic aspects of the word.
"Throne" is most obviously a sign of kingship. In this respect Revelation 4 is illuminating. When John gets his first peek of heaven, his whole focus is on the throne. It's the first object that John sees and describes. And we get the impression that it takes his breath away. The NIV translation of verse 2 says,
At once I was in the Spirit, and there before me was a throne in heaven.
This is correct, but boring. The old King James version brings out more of the sense of the Greek when it translates:
And immediately I was in the spirit: and, behold, a throne was set in heaven.
We get the idea of John saying, "The Spirit took me into heaven and ... Oh wow, look at the throne!" So throughout chapter 4 the throne is John's whole focus, the centre of his attention. This is reinforced by his description of the other elements in the picture. Every single object - God himself sitting on the throne, the thunder and lightning, the seven spirits, the sea and the rainbow, the creatures and the elders - all of them are described in terms of their placement in relation to the throne. So thematically John is emphasising that God is sovereign, God is in charge as we see the story unfold throughout the rest of the prophecy.
"Altar" also has its core meaning and symbolism, especially for Jewish readers. The altar is the place of sacrifice. It is where people make offerings to God, and in the Old Testament the sign of the altar surely points to God's holiness.
The altar is not mentioned in Revelation as often as the throne, but it seems to me that when it does appear it has this focus of sacrifice, offering and holiness. Thus in Revelation 6.9 the souls of the martyrs are under the altar because their death and their testimony are a sacrificial offering to God. And in Revelation 8.3-5 we read this:
Another angel, who had a golden censer, came and stood at the altar. He was given much incense to offer, with the prayers of all God’s people, on the golden altar in front of the throne. The smoke of the incense, together with the prayers of God’s people, went up before God from the angel’s hand. Then the angel took the censer, filled it with fire from the altar, and hurled it on the earth; and there came peals of thunder, rumblings, flashes of lightning and an earthquake.
Here there is a strong picture of an offering which rises up to a holy God, as well as judgment hurled down on a rebellious earth. The purifying work of sacrifice and of fire flows in both directions, and the altar is the centrepiece of this activity.
It's worth noting that this verse is the only verse in Revelation that refers to both the throne and the altar by relationship, and they are not in the same place. Here the altar is before the throne, and thus separated from it. (But then we are talking symbolically, and words that are distinguished in our language refer to a God who is one, who is fully integrated in all aspects of his activity and character.)