No. From oneworld.com:
Extra baggage allowance for Emerald frequent flyers
As an Emerald frequent flyer you can check in one additional bag for free in addition to your ticketed baggage allowance when you fly on oneworld airlines. If your ticket mentions a weight allowance, you can check in an extra 20kgs (44lbs). (This benefit is not available on British Airways 'Hand Baggage Only' fares on select short-haul routes.)
Extra baggage allowance for Sapphire frequent flyers*
As a Sapphire frequent flyer the following special baggage privileges will apply when you fly on oneworld airlines.
On international or domestic itineraries using the baggage allowance "weight" system you receive 15 kgs in addition to the ticketed Economy allowance.
On international itineraries (including domestic sectors flown as part of international itineraries) using the baggage allowance "piece" system, you will receive a second bag, weighing up to 23 kgs, when the ticketed allowance is one bag.
On domestic itineraries only with flights using the baggage allowance "piece" system, you are guaranteed at least one piece of checked baggage, weighing up to 23 kgs, even when the regular ticketed allowance has no free allowance.
Customers travelling in First and Business Class cabins will in most cases receive an even greater free checked baggage allowance.
*This benefit is not available on British Airways 'Hand Baggage Only' fares on select short-haul routes.
*For domestic routes operated by LAN Airlines, Sapphire cardholders may check in up to two bags with a combined weight not exceeding 23 kgs.
http://www.oneworld.com/ffp/extra-baggage-allowance
Individual airlines may provide a complimentary baggage benefit to companions of certain elite members. This is not a oneworld benefit.
For example, BA provides:
Executive Club Gold and Silver members and oneworld Emerald and Sapphire members receive additional checked-baggage benefits when flying on British Airways flights.
Executive Club Gold and oneworld Emerald members
•An additional free checked bag in any class of travel for the cardholder and any customer travelling on the same booking (excludes hand-baggage only fares and group rate bookings).
•A weight allowance of 32kg (71lb) per checked bag in any class of travel for the cardholder only.
Executive Club Silver and oneworld Sapphire members
•A checked baggage allowance of two pieces in any World Traveller, Euro Traveller and Domestic cabin for the cardholder and any customer travelling on the same booking (excludes hand-baggage only fares and group rate bookings).
•A weight allowance of 32kg (71lb) per checked bag in any class of travel for the cardholder only.
You will need to check the baggage policies of the individual airlines.