You could use this in Logic Pro X, but we don’t really recommend doing so because you will lose out on the real time modifier control of the sound. Being able to change the beat character by adding in different percussive elements and adjusting the tone in real time is one of the main highlights of Worship Beats, and you would not have this when you import the patches into Logic. If you are very advanced with Logic, you could separate the different percussive elements in a patch into multiple patches, and then record in that way- but that would be a bit tricky to set up.
You can however record a Wav of Aiff file directly inside of MainStage 3 by pressing MainStage’s record button. You could then move that file into Logic Pro X. Or, you could use a virtual audio cable such as SoundFlower to direct the audio from MainStage into Logic Pro X digitally.