If you have a very large monolithic database that is not partitioned or sharded, with strong relationships between the tables/data, does it still make sense to use microservices as the application layer?
No, it does not.
Microservices are meant to be loosely coupled and independently deployable. Having a single backing store introduces a single huge integration point that greatly diminishes loose coupling and ability to deploy independently.
You would greatly complicate the architecture by not gaining anything in return.
Also, having a single database would be way too tempting for developers to abuse it as communication channel between services instead of using inter-service calls.
Another big reason for microservices is failure impact reduction. When one service is down, it shouldn't result in the whole system going down. Having single database would introduce single point of failure, making microservices mostly useless.
data layer thats unlikely to change
One of the big point of microservices is to facilitate more agile and flexible changes in your software. I don't see how using microservices would help when their database would stay static.