The answer to your question really depends on what exactly you are asking.

If you are asking if you can solo mine with the goal of getting a transaction confirmed quicker then yes you can do that however this would really be a moot point unless you are trying to broadcast a transaction with either a 'lot' of inputs or a 'lot' of outputs and are not paying a sufficient fee.

If you are asking if you can mine so that the block reward goes to 'your' address, then this is what every pool (except eligius) does as the block reward goes to the pool's address and then the pool will in turn pay the pool's users. (or someone who is solo mining will simply have the block reward go to their own address)