The logger is part of the app, so the logger would also be gone along with the app. I presume the logger can only write to an area that is accessible by Starbucks app due to sandboxing. If the app is gone, I am not sure if that temporary area is wiped right away. Eventually it would be overwritten, but not sure how soon.
According to the original bug report, the log is at:
/Library/Caches/com.crashlytics.data/com.starbucks.mystarbucks/session.clslog