Yes, it would seem the comma is needed. This is the very distinction between coordinate and cumulative adjectives.
If two modifiers are describing the same feature (and would make sense with the word "and" between them) they are coordinate. The "and" should then be replaced with a comma. As long as the cumulative adjective isn't used to create a compound noun, the comma is needed.
The wealthy, elegant lady looks like a model.
In contrast, cumulative adjectives build upon each other and must be in a certain order. They don't take "and" or commas between them.
The big old black bull followed the young Brahma cow.
In OP's example, since single and unified are both modifying "database" in the same way (number/size), they are coordinate adjectives. The sentence would read correctly if written:
The company uses a single and unified database for all its customer
Therefore we can replace the "and" with a comma:
The company uses a single, unified database for all its customer