It is possible for a firm to engage in earnings management and still have a high quality of earnings, but it is not a guarantee. Quality of earnings refers to the reliability and transparency of a company's financial reporting, while earnings management refers to the manipulation of financial results to meet or exceed expectations.
In some cases, a company may use accounting techniques that are within the bounds of generally accepted accounting principles (GAAP) to achieve earnings management, while still maintaining a high level of transparency and reliability in their financial reporting.
However, in other cases, earnings management may involve unethical or illegal practices such as misclassifying expenses or overstating revenue, which would result in a low quality of earnings. In summary, while it is possible for a firm to engage in earnings management and still have a high quality of earnings, it depends on the methods used and the transparency and reliability of the financial reporting.