First of all I'll be controversial and say that non-diabetic pregnant women should not be very low carbing (<25% energy), the area is not well studied and the few studies we do have are concerning. Sorry guys but it's totally experimental and pregnancy is not the time to be conducting these types of experiments.
Second of all where did the 2/3 false positive thing come from? From the Hyperglycemia and Adverse Pregnancy Outcomes study, we can see a linear effect in negative outcomes and failed OGTTs.
I would definitely do the test, if low carbing (which again I do not advise), carb up for a week before the test. If a positive test occurs, then how you handle that is up to you.
Bottom line is hyperglycemia is far more likely to happen during pregnancy due to an increase in certain hormones and it is something that needs to be tested for.
Just finished my thesis on GDM so if anyone needs more info/links to studies let me know.