Possibly, assuming Zion succeeded in killing everyone plugged into the Matrix. It depends on how the Matrix was destroyed and the strength of the humans vs. the machines afterward. But the Matrix is very well defended both from within and in the real world, so it would be almost impossible for Zion to succeed.
Killing all the humans plugged into the Matrix (and committing genocide) is essentially Zion's endgame, so morality is not a factor. Morpheus admits in The Matrix Online that Zion's stated goal of destroying the Matrix would probably result in the deaths of millions1:
We thought... I thought... we could win this war or lose it. If we won, yes, millions would die in their pods, but our days and years would be spent saving those we could, and reclaiming the surface. Instead, we have peace. Neo found a way to save them all...
This would drastically reduce the amount of energy available to the machines since their source of energy depends on humans:
Morpheus: The human body generates more bio-electricity than a 120-volt battery and over 25,000 BTU's of body heat. Combined with a form of fusion the machines had found all the energy they would ever need.2
The Architect does say that the machines are prepared to survive without the Matrix:
The Architect: ...Failure to comply with this process will result in a cataclysmic system crash, killing everyone connected to the Matrix, which, coupled with the extermination of Zion, will ultimately result in the extinction of the entire human race.
Neo: You won't let it happen. You can't. You need human beings to survive.
The Architect: There are levels of survival we are prepared to accept.3
However, the Architect's claim that the machines could survive the destruction of the Matrix is made in the context of the hypothetical scenario in which the machines had just exterminated the human race. In that case, the war would obviously be over and the machines could power down all non-essential machines (in particular, their war machines like sentinels and the Armada).
What would happen if Zion succeeded in killing everyone in the Matrix?
In the scenario you pose, Zion would still exist and would be able to continue the war against the machines in the real world -- so the machines probably wouldn't have enough energy to power 01 and all their war machines. A significant portion of the massive machine army would have to be powered down, giving Zion a much better chance at defeating the machines.
Still, the machines could power down all portions of the machine army that are not actively deployed against Zion, and they could power down non-essential machines in 01. This would help reduce the machines' power usage so that they would not run out of energy as quickly. Also, as noted in another answer, the machines might still be able to use power from the fetus fields.
The machines would need to launch an attack against Zion immediately in order to end the war soon so that they could power down the rest of the machine army. Any machines destroyed in those attacks would no longer need power, so deactivated war machines could then be powered up and used in their place without increasing the net power usage.
Meanwhile, Zion would need to wage a defensive war of attrition: if the machines don't attack they'll eventually run out of energy, so Zion would let the machines attack and use the advantage of defense to wear them down.
The victor would be determined by battlefield success, how much energy the machines had stored up prior to the loss of energy from the Matrix, and how low the machines could bring down their net power usage while waging war against Zion. We don't know who would win that.
But the machines have ensured this would not happen
As explained by the Architect in The Matrix Reloaded, Zion is intentionally created by the machines at the beginning of every cycle of The One. Zion is a form of control in which The One chooses an initial group of "red pills" so that they can unplug the 1% of the human population who reject the Matrix; this stabilizes the Matrix by removing the people who reject it, and allows the red pills to find the next One in order to restart the cycle. The machines allow Zion operatives to hack the Matrix -- the Matrix can actually be defended very well both inside and out.
The Matrix is protected from the inside by Agents, and there are many more than just the few Agents we see in films. Zion operatives would require a great deal of coordination to cause a major cataclysm and, as you suspect, these Agents would be able to prevent them from succeeding.
Even if Zion somehow managed to coordinate enough operatives to overwhelm the Agents, the Matrix is protected in the real world by sentinels. Again, the machines allow Zion operatives to hack into the Matrix -- if needed, the sentinels could prevent any operatives from entering the Matrix. If the Agents were somehow overwhelmed inside the Matrix, an Agent could order sentinel strikes on Zion hoverships. The machines have a massive sentinel army, and in The Matrix Reloaded this sentinel army does start to restrict the ability of Zion hoverships to get into position to hack into the Matrix:
Morpheus: ...My apologies to all. As you are undoubtedly aware, it has become increasingly difficult to locate a secure broadcast position.
Vector: Squiddies got all our best spots.
Ice: Mainlines are crawling with them.
Ghost: And if Niobe's right, in 72 hours there's gonna be a quarter of a million more.
Ballard: What are we gonna do about it?
Niobe: We're gonna do what Commander Lock ordered us to do. We'll evacuate broadcast level and return to Zion.4
With the Agents inside the Matrix and the sentinels guarding it in the real world, the machines could make it nearly impossible for Zion to even hack into the Matrix, much less cause a major cataclysm.
1It would actually result in the deaths of billions.
2 The Matrix
3 The Matrix Reloaded
4 The Matrix Reloaded, partial conversation from the Crisis Meeting