Most brokers have a minimum distance to set your take profit. You could theoretically write an EA that manually closes 1 pip into profit. The drawbacks are large - any stoploss would need to be larger. Even a manual close after losing 1 pip would mean that you would lose at least 2 pips (assuming only a 1 pip spread - you risk 2 pips or more to try to make 1 pip). Your trades would be VERY quick, tempting brokers to accuse you of breaking trading rules (results in ALL profitable trades being deleted, and maybe the losing trades, maybe not).
Combine all of that with the possibility of requotes or slippage and I can't picture there being much chance of coming out ahead.