For instance I am using BoneCP for connection pooling in my application, hence it creates 30 connections in connection pool with the remote Database, now if at the same time at different machines, suppose 10,000 instances running, each instance creating 30 connections and accessing the remote DB, does it creates any issues like accessibility, connection problems, or load, stress etc on remote DB.
No actually too many active connections with a remote DB isn't the problem, the problem lies in the Configuration to access the Remote DB, For instance Azure allows only 100 connections Simultaneously, hence when more then 100 connections we try to create in our connection pool then there will be no connections made once the limit reaches.