Unfortunately, no. One cannot be addicted to doing good. When one is addicted to something they have developed a dependance on that thing; it controls them (meaning they think they can't live/survive without it).
If one does something constantly for a long enough time, it becomes ingrained in them. We call this a habit. Habits can be good or bad. Brushing your teeth every day is considered to be a good habit, while biting your fingernails is considered to be a bad habit. Some people get into the habit of always being truthful and honest. We say these people have integrity. Others don't get into this habit as they don't practice it continually. They intermix honesty with telling lies and being deceptive. Even though some habits can turn into addictions (smoking, lying, drugs), we don't call continual good habits addictions. We don't say that someone is addicted to saying 'please' and 'thank you' (not including OCD). Rather we say that that person has developed a habit of being polite. The word addiction denotes negativity. We don't want to be addicted to anything. However, we do want to form good habits.
Forming a good habit takes effort while developing a bad habit doesn't seem to take any effort at all.
Both habits and addictions can be broken. While good habits are fairly easy to break, it takes strength and determination to break a bad habit or addiction. More effort than developing a good habit in the first place. Addictions can also be broken, however breaking them may require the help of others.
WM BARR . =ABSOLUTE TRASH 