Having to know Luganda - or any of the other languages of Uganda - depends on what brings you here, which businesses you have. For medical personnel it is very useful to speak the local language. Among the business people in and around Kampala, English or the Ugandan version of English is widely spoken. English and Luganda are the national languages, but not spoken in all corners of the country.
I've been living in and out of Uganda for many years and apart from a few words never managed to learn Luganda, Ryankole or Luo/Acholi. Yet I am well integrated in the Ugandan society, live among the Ugandans and rarely go to places where mzungu's gather. I know how to greet and say 'thank you' in the main languages of Uganda.
Integration in a different society is not only about speaking the same language, but also about having respect for the differences in values, cultures and habits of your host country.