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In the short term, maybe. In the longer term though, I don't think that's likely, for a few reasons:

Reducing sunlight reaching the earth a bit to cool it down only counters one environmental issue, rising temperature. That one issue may be the most dangerous one, for us, but it's isn't the only one, and so even if we just threw up our hands and stopped worrying about fossil fuel use, there still would be worsening consequences to other environment issues, like habitat loss, ocean acidification, soil erosion, overfishing, microplastic and other pollution that is not just a greenhouse gas, etc. Dealing with these issues, or the problems resulting from them, would force environmental issues to stay in the public consciousness. Some may even be made worse by whatever method we use to darken the sky, and so there will be incentive to use that technique less if we can manage.

Certain mitigating factors, like renewable energy in particular, have already progressed to a point where they are more profitable than fossil fuels in some cases. This should inevitably lead to an increasingly large industry around those things. This would both slowly force a transition away from fossil fuels anyways for the sake of profits, and also lead to a large industry whom harsh regulation on fossil fuel benefits, due to that harming their competition. Such industry could lobby for regulations that benefit their interest just as other industries have.

Fossil fuels are finite. Technically all energy resources are on some scale, but fossil fuels are limited on a much more human scale. Eventually, the oil and gas and coal will run dry, and long before that happens, it will get too expensive to keep using increasingly difficult to extract deposits for energy. Thus, while we would in almost any scenario need to maintain a geoengineering scheme for a long time, we would not need to maintain it forever. Unless we decide to use it not just to keep the climate from warming but to also change it into something that benefits us more than the previous natural climate did I suppose, like some kind of mild terraforming on earth itself, but if we ever had climate engineering developed to that degree, we'd probably have enough experience at it and what it's pitfalls and limits are that keeping it up indefinitely is no longer a problem anyway.