No. Even if you run a full node, the propagation of the transaction will depend on others, not you. You might be able to accept your own transaction with a very low fee but if others have their minimum relay fee threshold set high, they wouldn't relay it. Poor propagation means that the miners would have a low chance of seeing it.

In the end, it depends on the miner. They can choose to include transactions with low fees or high fees into their block. Nodes can't have a say.
A full node also function as a wallet.