Not really.
Assuming a heliocentric solar system, if the Earth's rotation were stopped, both the sun and the moon would continue to have slight, but real apparent motion in the Earth's sky. The sun would move as a result of the Earth revolving around it, and the moon would move as a result of it's revolution around the Earth. (Both of these motions depend on mass only, and not rotation.) Further, the Sun has apparent motion associated with the Earth's axial tilt, and the fact that the Earth's orbit isn't a circle, but an ellipse.
For the Sun to appear to stop in the sky, the Earth's rotation would have to slow to one rotation per year, the Earth has to be untilted, and the orbit has to be altered to be a circle.
But the moon is the real problem, here. For the moon to appear to stop, it's period of rotation and revolution must be equal, and it must be in geostationary orbit about the Earth. For the earth rotating at it's current speed, that is about ten times closer to the Earth than it is now. The moon orbiting at such a distance would dominate the sky.
However, in this problem, remember, the Earth's rotation has to be slowed down to one revolution per year. But at such a rotational speed, geostationary orbit is significantly farther away from the Earth than the moon's current distance. (As an alternative, you could move the moon to one of the stable LaGrange points in the Earth-Sun system.) So you would not only have to move the moon a significant distance, but you would also have to slow it's rotation significantly, as well.
And, at such a distance, the moon would appear to be tiny. Of course, this movement of the moon would be a movement, so the moon would not be standing still, as the passage in Joshua suggests. And there is nothing in Joshua which notes the Moon's sudden change in size. That would be as remarkable as the Sun and moon not moving, and would surely be noted.
However, assuming a geocentric solar system, on the other hand, in order for the sun and moon to appear to stop, they merely have to stop (and the moon would have to stop rotating.) (This, of course, discounts the effects of gravity as we know them, but that is consistent with this model, anyway...)
The point is that, with a heliocentric model, it is impossible to get the Sun and the Moon to appear to be motionless simply by halting the motion of the Earth. And it is impossible to get the moon to remain the same apparent size in the sky and be still just by stopping the motion of these bodies. It would require massive and multiple re-calibrations of the Earth's rotation, axial tilt, and orbit just to get the sun to appear to stop, and the moon is an even bigger problem.
The passage in Joshua is clearly more consistent with a geocentric understanding of the solar system.
That stands to reason since the biblical texts were written by, and for, a wholly geocentric audience.
One of the simple apologetics books I read a long time defined the term miracle as "An occurence which is contrary to physical laws", i.e., a dropped baseball stopping in midair with no obvious impediment (such as a hand, glove, or suspension device.
While what was being described in Joshua is a "simpler trick" assuming a geocentric system, the occurence itself, in no matter what type of system is beyond that possible within physical laws (at least as currently understood).
I was trying to keep the "miraculous" aspect out of my original reply, since this is not on the religion forum, but thanks for your pointing out how much harder God had to work to answer Joshua's prayer! ;-)