Unknown (but probably not)
No one who we can trust to provide ratings has provided a ranking for the fusion. Nor has there been any omniscient-narrator provided rankings, such as a text box which simply asserts their threat level without being dialogue.
There are two things that might weigh against being a God level threat:
- Not quite world-affecting. While it can impact a geographically large area, it still seems limited to at most continental level impacts, and most of that just seems to be exploiting the physics of wave propagation, and is largely minor over most of that area. She hasn't done or affected much more than what we'd expect of a strong earthquake.
- Tatsumaki can handle it thus far. Blast is the God-level threat insurance plan, while Tatsumaki is the everything-else insurance plan. Tatsumaki has thus far shown no signs of feeling overwhelmed or out of her league, even when she's out of the sight of others and no longer in need of maintaining her image. And Fubuki continues to undergo a mental breakdown over the absurd level of power, without really fearing for her sister's well-being. Tatsumaki is also able to neutralize the tsunami by simply carving out a massive trench ahead of it. And then hurling what she carved out at Psykos-Orochi in a massive barrage, all while showing no signs of exertion or stress whatsoever.
So Psykos-Orochi doesn't seem to be generating any threat more extensive or powerful than Tatsumaki herself can generate (with apparent ease). So unless we accept that Tatsumaki is herself at God-level, even given that she respects Blast and seems to acknowledge him as the greater power, it seems safe to reject the idea of Psykos-Orochi being a God-level threat.
The main reason for thinking she might be one seems to be that the power range on Dragon level threats would appear to be gargantuan otherwise. But as we've already seen it acknowledged that the threat rankings are a flawed system, and in fact has undergone revisions before to account for the emergence of even more powerful monsters, this may simply be a deficiency and shortsightedness of the system. And, indeed, the scale difference between "city-wide threat" for Dragon (such as the meteor) versus even just a country-sized effect is itself gargantuan. The City of Los Angeles is about 501 square miles, whereas the area of, say, France is just short of 250,000 square miles. That's about 500 times larger by area. And LA is a very large city: Paris, France is only a hair under 41 square miles, less than a tenth the size of LA and less than 1/5000-th the size of France.
As such the apparent power range on Dragon threats may be an example of the "Writers have no sense of scale" trope in action, resulting from a failure to grasp just how large the scale differences between city/country/continent/world are. Alternatively, it may be an intentionally logarithmic scale, like the Kardashev scale for galactic civilizations: Type 1 is "society uses an amount of energy equal to the solar energy incident upon Earth" which is already about 10000 times what our modern day society uses, while Type 2 is "uses an amount of energy equal to the sun's entire output" and is many orders of magnitude larger, and Type 3 is many orders of magnitude beyond that. Thus the massive range in power for Dragon level threats may be an intentional design feature, reflecting how the next meaningful scale beyond it is massively larger.