Is pre-mining of a future block possible? Is it possible to pre-mine next block when everyone is mining current block? 

Let's say, if we need 1T hash power to mine (solo / pool) a block in 1 hour, then is it possible to run 1G hash miner for 1000 hours and then use this data as proof of work.

With 1G miner, I am essentially targeting n'th (x + 6000) block in future, hoping to solve it. I will broadcast it as soon as I get hash of n-1'th block.
You seem to be asking if you can mine block X+1 while the network is still working on block X.

The answer is no, you can't mine block X+1 until block X has been solved, as each block requires a hash of the previous block to be valid.