Yes, a sick person's dua (supplication) is highly likely to be accepted by Allah.
According to Islamic tradition, the supplication of a sick person holds a special significance and is less likely to be rejected. This is based on a hadith (saying of the Prophet Muhammad ﷺ) reported by Ibn ʿAbbās (may Allah be pleased with him), where the Prophet Muhammad ﷺ said: “The supplication of the ill person is not rejected, until he recovers.” (Reported by Ibn Abī Dunyā & al-Bayhaqī).
This hadith suggests that during illness, a person is in a state of vulnerability and increased dependence on Allah, which makes their prayers more readily accepted. The illness itself can be seen as a purification and a test, during which Allah is particularly receptive to the person's supplications.
Therefore, if you are sick, it is strongly encouraged to make dua, not only for recovery but also for any other needs and desires. Allah's mercy is vast, and He listens to those who turn to Him in sincerity, especially during times of hardship.