I don't think they count as science...until the make predictions that match the later observed results. Then they do.
Unfortunately, as you pointed out actually recreating the simulation can be absurdly difficult. And if it's not reproducable, then it's not science.
That said, when I worked at a transportation study commission, we used models all the time. We never deceived ourselves that they were correct, but they were a lot better than just guessing. Policies were built based around their 20-year projections. Often we'd have several very different 20-year projections based on different assumptions about what would be done in between. (Would this transit project be successful? Would that bridge be built? What effect would building the other highway have on journey-to-work times?) The results were never accurate. They were subject to political manipulation...but so was what projects would be built. It was a lot better than just guessing, but it sure was a lot short of science.
I think of this frequently when I read about the models, and the problems that people have with accepting their projections. Usually the problems aren't based in plausibility, but rather in what beliefs make them comfortable. And in those cases I tend to believe the models. But I sure don't think of them as "sound science".
OTOH: Do you trust the "Four Color Theorum"? It's a mathematical proof that any map can be colored with four colors, with no two adjacent patches having the same color except at a single point. The proof is so complex that no human can follow it. Do you trust it? Would you trust it if a lot of money was riding on the result?
Even math is less than certain. Complex proofs are only as trustworthy as every step in them multiplied, and both people and computers make mistakes. There are lots of illusions that prove that people will frequently dependably make the same mistake. So you can't really trust math. But just try to find something more trustworthy. You need to learn to live with less than certainty, because certainty is always an illusion.