That may be. Unfortunately, if it's unlocked, I'm guessing your carrier is someone other than a provider than regularly stocks and sells this device. If that is the case, then your provider will not have a "test battery" lying around the store for you to check your suspicions. The stores that will (AT&T for example) probably will not let you test the issue since you are not using their service.
Of course all this is simply a guess, and I suppose it's worth a shot, but I would avoid buying a new battery until you are able to ascertain that your suspicions are, in fact, true.
RETIRED: 7230, 7290, 8700G, 8320, 8900. 9000 BOLD