Do unfinished essays cause the essay readers to lower your score? I ran out of time on my last SAT, and while I think most of my essay was excellent, I wasn't able to complete it.
The short answer is yes, probably. It will depend on how much of your essay you were able to complete before running out of time, of course - an essay with well-explained, concrete examples will still do pretty well without a conclusion. But if you ran out of time to mention as many examples as you wanted to, or to flesh out your examples with supporting reasoning, that's going to have a negative impact on your score. And if your essay doesn't make sense because it lacks a conclusion that ties everything together, that will also lower your score.
The longer answer is that the current SAT essay (March 2016 and later) is scored across three different areas - Reading, Analysis, and Writing. Because of this, it's possible to get high scores in Reading and Analysis and get a lower score in Writing because you omitted an introduction and conclusion. On the other hand, if you ran out of time to analyze the prompt as thoroughly as you would've liked but still managed to write in a detailed fashion about the content of the prompt, with an introduction and conclusion, you'd be able to score highly in Reading and Writing (and would get a lower Analysis score).
In either case, however, the graders aren't going to "lower" your score if you fail to finish your essay, because the essay isn't graded in a way where points are taken off for a defined number of errors. Instead, graders are given what are called "anchor essays" at each score point and use these to inform their grading. As our article on how to get a perfect 8/8/8 on the SAT essay explains, essays at each score point meet certain criteria, but the weight the grader gives each criterion is demonstrated not through explicit instructions, but through those anchor essays (and how the criteria manifest themselves in actual writing).
In conclusion: if you ran out of time and didn't get to finish your essay on the SAT, you might get lower scores in some scoring areas than the others, but since there isn't one overall essay score any more, it's possible that the damage might only be limited to one of your essay scores.