Can any one clarify whether (or, not) an increase in mining pool in Ethereum network with decrease the average block generation time? (For example, if another pool like ethermine join the network today and start mining). Since all the pools are competing with each other, I am getting confused
No, block generation times are driven by the current difficulty for solving the the algorithm used in the Proof of Work model. Only when a solution is found, is the block accepted to the chain and the difficulty determines how long it will take to find that solution. This difficulty automatically adjusts to speed up or slow down block generation times.
From the mining section of the Ethereum wiki:
The proof of work algorithm used is called Ethash (a modified version of Dagger-Hashimoto) involves finding a nonce input to the algorithm so that the result is below a certain threshold depending on the difficulty. The point in PoW algorithms is that there is no better strategy to find such a nonce than enumerating the possibilities while verification of a solution is trivial and cheap. If outputs have a uniform distribution, then we can guarantee that on average the time needed to find a nonce depends on the difficulty threshold, making it possible to control the time of finding a new block just by manipulating difficulty.
The difficulty dynamically adjusts so that on average one block is produced by the entire network every 12 seconds.
(Note that the current block generation time is closer to 15 seconds. You can find the block generation times on Etherscan)