At least one study indicates, tentatively, that the answer may be a "yes."
The idea of helping ensure the best teachers are paired with the weaker students makes a lot of intuitive sense. It's been among the policy proposals stemming from a renewed focus on teacher evaluations.
For instance, in agreeing to accept 2009 economic-stimulus legislation, states had to pledge to take steps to improve their teachers' effectiveness, and, borrowing a formulation from the No Child Left Behind Act, to ensure an "equitable distribution" of high-quality teachers between high- and low-poverty schools.
At the same time, scholars have also suggested that value-added measurements can be influenced by factors such as a teacher's peers, and by other cultural factors within a schools.
To tackle this question, researchers Zenyu Xu, Umut Ozek and Matthew Corritore analyzed up to 11 years of longitudinal test-score data tied to teachers from North Carolina and Florida. They looked at nearly 70,000 teachers as a part of the study, and categorized them in one of three groups: Teachers who did not switch school assignments; those that moved to a school with a similar performance or poverty levels characteristics as the one they left; and those that switched to a school with substantially different such characteristics. They also tried to control for factors, like teacher experience and the "peer" effect reference above, in their analysis, which was published by the National Center for Analysis of Longitudinal Data in Education Research.
The most important finding: Across all of the different models, the scholars found that, on average, strong teachers who moved to a disadvantaged school weren't penalized by teaching lower-performing students. Instead, they continued to get good results with students, outperforming those low-performing teachers who transferred.
The findings stand somewhat in contrast to a previous study, which called into question the portability of teacher effectiveness across schools.
In the paper, the scholars caution against overgeneralizing their findings. They warn that the findings are conditioned on current, often seniority-based transfer policies that may resulted in a transferring population not representative of the population at large. (It's a similar problem to selection bias.)
Though it's early yet, federal officials have commissioned a study examining a similar set of questions about teacher effectiveness. Called the Talent Transfer Initiative, it will hopefully flesh out and add to the research literature on this topic.