Its very difficult to tell, because I have no idea what the character test is.
If Im wrong on this someone please fill me in, but it is my understanding that Demarcus Cousins is the only star we have chosen not to pursue based on character concerns.
There was reported(not that that means much) interest in Dwight Howard at the deadline and in FA this year.
There is also the longstanding rumors of interest in Jahlil Okafor(tried to fight a fan in Boston)
Lets also keep in mind, Marcus Smart pushed a fan in college, Isaiah Thomas had teammate issues in Phoenix(although they werent his fault), and Evan Turner was hugely unpopular in Indiana.