Using corrosion inhibitors in the OWB loop will also prevent any corrosion in the pump, by converting the pH to a level that prevents the steel and/or any other metals from oxidizing. As someone said above, in an open loop boiler system (non-pressurized) there is always O2 getting into the boiler water from the vent.
There are two types of Ox barrier PEX: one has a polymer laminated to the outside surface (or sandwiched between the PEX layers) that prevents oxygen from penetrating. The other type has a layer of aluminum embedded between layers of PEX to provide an oxygen barrier. Ox barrier PEX is designed mainly for using in applications that are sensitive to oxygen, like closed loop pressurized hydronic floor heating systems with metal pumps.
In an OWB non-pressure loop, you don't need it. Plain PEX will work fine. Ox barrier PEX is said not to flex and/or expand and contract as much as regular PEX does though. So in some cases it might be better if expansion is an issue.