Yes, and that is one of the huge problems with it. One developed country can do geoengineering that affects everyone, for better or worse. One developed country can decide to take the risk regardless of the rest of the world.

If my relatively well off country decides to spread some aerosol in the stratosphere to reduce incoming solar, for example, it can likely afford to make a difference in the rate of climate change. But just by calling it climate change, we’re recognizing it could affect everyone. Whatever I’m pumping into the stratosphere will not stay within my borders. If I’m able to change climate patterns in my country, those changes do not stop at the border

And of course a related issue is that any intentional change in climate systems will have different effects in different places. Even if you succeed, there will inevitably be those worse off. You can easily picture this turning into an out of control conflict. We all know about historical atrocities around resource exploitation of less developed countries, so what do you expect will happen if weather patterns are intentionally changed to benefit the climate of the wealthier countries at the expense of those who can’t afford it?