The answer is, at agricultural scales, absolutely not. What I think is interesting though is that your comment on "hydrological warfare/competition" is extremely relevant. Geo-engineering is almost always a hack with "no free lunch" impacts. For cloud seeding specifically, there is only ever so much water vapor available in the atmosphere and the efficacy of seeding depends on the dynamics/microphysics at play in the region of interest. If there is a lack of the specific aerosols necessary for condensation and precipitation, cloud seeding has shown to be effective to the tune of 5-15% increase in precip in certain regions. Water vapor doesn't like to hang out available in the atmosphere in large quantities so squeezing it out by forcing precipitation via "seeding" isn't really a reasonable concept. But to the degree that you do succeed, you are extracting water vapor that would have been transported by the atmosphere to other neighboring regions.
While there is little evidence that cloud seeding can be done at-scale, in a world where someone comes up with a novel+clever idea this would mean that the impacts on precipitation in other regions would be significant. Again, no free lunch. It's not a stretch to imagine turning that into a competitive advantage or using it as a warfare tactic.
If there were large bands of moisture just waiting to fall out of the sky we would be living in a very different climate. Aerosols are far too common on earth. In fact, the Arctic is one of the only places seeding makes a lot of sense with supercooled water and a distinct lack of aerosols in the clean environment. But in my research I have yet to come across much agriculture up there much less agrarian societies ;)