Does /dev/block/mmcblk0 include an external sd card that has been formatted as internal? I am performing a backup using the following command with a su shell:

dd if=/dev/block/mmcblk0 of=/mnt/expand/ee131623-1634-25d1-9f9f-902b68eceaee/mmcblk0.img"

And I was wondering if this would fail to complete as it would include the backup in the backup?

Is Internally formatted external sd cards included in mmcblk0?
No. Internally formatted external sd card is not included in mmcblk0. dd dumps files, in your case the block device file mmcblk0 which includes all partitions, GUID partition table (GPT) and any free space in between partitions.

External SD card is a separate flash memory chip, so exposed by a different block device available at path something like /dev/block/mmcblk1 or /dev/block/sda.