Hi Jeff,
There should be no problem restarting MySQL while DM is running. When the local DB goes offline, DM will go into offload mode. This means all data that needs to be forwarded to the DB will be stored in files temporarily. Once the DB is back online, DM will push the files from the offload folder towards the DB. and then start to communicate again directly to the DB. If your DMA would restart with offload files in the folder, it will only do the startup after all files have been pushed from the offload folder. This is to ensure DM starts with the latest data. So if you have a lot of files in the offload folder the startup might take a lot of time. When you want to ensure fast startup and you know there are no important parameters changed recently you could move the offload files to have a faster startup.

Let us know if you have other questions related to this.