In small amounts, yes. Electrolyzed water is simply water that has had electrolosis performed on it from what I can tell. (http://www.aquatechnology.net/electrolyzed.html). All you need to do this at home is a cup, 9-volt battery, couple of wires, some salt, and of course, water.

Fill the cup up, and mix in the salt. Strip the ends of the wires and attach to the + and - of the 9-volt battery, and place the other stripped ends into the glass (Not touching!). After a moment you should begin to see small bubbles around each of the wires...this is Hydrogen and Oxygen being broken apart in the electrolysis reaction.

This reaction has been common in HS classrooms for years. Teachers collect the hydrogen in a test tube or beaker (it's lighter than air, so holding it upside down is sufficient), and then light it on fire as hydrogen is combustible when mixed with O2.

If you collect both Hydrogen(H2) and Oxygen(O2), this will mix to for a gaseous mixture called "Brown's Gas". This is HIGHLY combustible, and you should probably handle it with some care. Unless you collect a LOT, it's not going to do much harm...but better safe than sorry.

Electrolyzed water is the left over product after you have pulled some of the gas away. The salt(NaCl) that you mixed in will react and form HCL, which when allowed to stay in the water solution forms a weak Hydrochloric acid. This can be used as a cleaner. The longer you allow the reaction to take place, the more HCL is released, and more acidic the solution becomes(to a point). You may notice a slight greenish tint to the water after a while...this is from the chlorine.

NOTE: The only reason salt is used in this is because water on it's own is not a very good conductor of electricity, so the voltage needs something to jump across...salt works well, and is cheap.