Yes. I believe Heath Ledger quotes should be used in a motivational setting, because I don't see a reason why they shouldn't be used in a motivational setting. If there is a particular quote from Heath Ledger that is inspirational, then there is no doubt that it should be used in motivational setting.
If they are motivational, then I see no reason why they should not be included in a motivational setting, especially if they are particularly pertinent to the situation at hand. I realize he died in a tragic way, but we still read the works of people that died in horrifying ways. There's no real reason to shove motivational sayings aside because of that.
I do not see a problem with using quotes by Heath Ledger in a motivational sense if those quotes are indeed motivational. Just because a person had problems in their personal life does not mean that their thoughts while alive are any less important or that they should be censored or not used, if there is a purpose.
No, Heath Ledger quotes should be not used in a motivational setting because his death is deflating emotionally. A part of motivation is lifting a person's spirits. Since Heath Ledger died from a drug overdose, any quote by him is tainted by his untimely demise and the situation surrounding it. This has a negative impact emotionally, and in turn, is de-motivating.
If anything, Heath Ledger's life should be used as an example of prescription drug use gone awry. His Hollywood lifestyle shouldn't be idolized because no one knew how many drugs he was taking and his doctors had no clue that his pills would kill him. Yes, his overdose was accidental. However, Ledger's lifestyle shouldn't be mimicked to assume that if you take this pill your life will be fine. Ledger needed to take a break and get sleep, he didn't need 10 prescriptions to help him get rest.