I highly doubt it. There is plenty of politics on the court, but none of it is this nakedly Machiavellian.
The political differences and similarities among the justices exist alongside other similarities and differences regarding issues like judicial methodology and intellectual temperament. Even when two justices agree on an outcome, they might do so for different reasons, or emphasize different aspects of the case. Also, cases that seem politically very fraught to outsiders often involve very narrow or arcane legal issues, and it’s often the case that these are far more relevant to how the case is decided than the political leanings of the justices.
You can sometimes see these issues in the opinions and concurrences and dissents. For example, in one of the cases about Trump’s tax returns, Gorsuch and Kavanaugh agreed with the overall judgment of the majority, but wrote a concurrence explaining that they would have reached a similar result using slightly different reasoning.
Also, as QuickSilver says, no-one can fire them, and they can’t be voted out, so there’s no particular need to demonstrate their honesty.