No, PostGIS is not necessary, but if it's available, it would be an option.
It's more likely that you have a partial PostGIS install in the template
database, and that's what's causing these errors.
Upon establishing a connection, the sde code determines what if any version of PostGIS is installed on the Postgres instance, the message you posted, is an indication that no PostGIS version is installed. It does not mean that you need to install it nor that anything is broken it is just a bit of discovery by our code when connecting.