Hi,
Just to confirm, are you saying that MS Sql Server services are running under Network Service Account and if changing that to Local Service Account would help ?
=> If this is what you are asking then NO, it doesn't matter which under which account the service runs.
What matters is if you have configured "Sql Server Authentication" for your database or not.
If you have configured only "Windows Authentication" for your database and don't have any other USERS using "Sql Server Authentication" then you will NOT be able to communicate with this server from Policy Server.
If you haven't already created a Sql User please create one by logging into Sql Server Management Studio --> Security --> Logins --> New Login as below , and use this credentials to connect to the audit database form Policy Server

Hope this helps,
Ujwol