Maybe, a little bit, apparently(?)...
Based on the only clear evidence I could find, i.e. a couple of online video clips, there are, perhaps, at least two instances of such use of the song in question, one in Kenya and the other in Tanzania, which happen to be the two countries in which Kiswahili (the Swahili language) is most widely spoken.
On YouTube, the video from Kenya comes from the Kahawa Sukari Baptist Church's channel, where it is entitled "Baba Yetu by Peter Hollens" and its description reads, simply: "Kahawa Sukari Baptist Kids singing along to Baba Yetu".
Peter Hollens, an American, is one of the "various YouTube artists" listed as having performed the song according to the Wikipedia article to which your Question is linked. It's unclear what relationship he might have to the church. He has been to Kenya at least once some years before Kahawa Sukari Baptist published their video (Oct 19, 2016) which credits him (presumably because they're singing along to his 2014 track). He offers them a counter-acknowledgement in the Comments section of their video.
It's difficult to tell whether the video represents a regular occurrence at the church or rather is a special performance specifically for the video. The children's dance routine accompanying the music incidentally matches the one in the video from Tanzania, entitled "Baba Yetu - Gospel Choir in Dar es Salaam, Tanzania". The only additional information thereon is that the video is published (Feb 17, 2011) by African Solar Rise, which "is a German-based non-profit organization" connected with the generation of solar energy.
Beyond this it is quite difficult (viz. impossible?) to prove the negative that the song is in fact not used by African churches (an extremely vast scope, even if we narrow it down to only "the Swahili-speaking African church," since that covers no less than six countries, and even up to nine if we include the fringes of Mozambique, Malawi and Zambia to which the spread of the language extends), at least not without some kind of in-depth survey on this particular song in that region's churches.
For whatever it's worth, I lived in the region for some years after the song's release, and interacted with various church circles, but I had never heard of the song before reading this Question. This is probably not saying much, however, since I'm just one person, and the area in question is huge. In one neighbourhood I lived in there were no less than five little churches in a 1-Km radius. For all I know, at least one of them did use this song.