Probably not likely, Spotify does not have much in the way of LDS music anyway, and there are several reasons for that.
One is that some musicians feel that Spotify 'doesn't pay its share' of royalties to musicians for playing their music, and at least one major LDS musician, despite the obvious missionary possibilities of his songs being on there, does not submit his music, and the musician is well-known too. It's the same reason we can't find anything half the time on Pandora or any other music service.
We do have Mormon Channel's music feed, and in the over 30 years LDS music has been on the radio whether it be over the air or Internet, we've never had it better than what Mormon Channel has done with music. Biggest playlist around, it will only grow from here, and they air far more music in a day than a typical over the air broadcaster would if they ran a similar format.
We do have 'on-demand' streaming, just go to gcmusic.lds.org or youth.lds.org (once there, look for 'Music' on the right). You can play any track, either singly, as a straight playlist or shuffle it. Over 300 General Conference music items, 150 youth music items, and some miscellaneous matter around the Church websites. The hymns are only on-demand as part of the Interactive Music Player, though.