In a half wave rectifier only a single diode is present. One end of the secondary wire of the transformer is connected to the p side of diode while the other to the load resistor. The n side is connected to the load resistor. When the diode is reverse biased no current passes through it. But current does pass through the other wire of the secondary which eventually meets the load resistor . So wouldn't the output in this case be an ac current?
Yes, it would be no DC in a strict sense. If the resistor is ohmic and the diode ideal, the current would look like a sine wave, where one half is set to zero. Though it would not be an AC, if AC is interpreted as strictly sinusoidal (with full wave). Sometimes this kind of waveform is called "pulsed DC", especially if a smoothing electrolyte capacitor is put in parallel to the resistor.
A current does not flow simply because you make a connection; you have to make two connections to form a circuit. When the diode is reverse biased it is like a switch being open, current cannot flow. When the diode is forward biased it turns on to complete your circuit.
The output through the load looks like this:
The diode blocks one polarity of the AC cycle but allows the other polarity through.