I've had an email exchange with Google Adwords support, in which they have stated with some certainty (they went off and consulted their "technical experts") that the fact that the "google_conversion_label" field is hardcoded to the value "purchase" is likely to be causing under-reporting of conversions.
The field is intended to select a "conversion type" for the conversion to be recorded against. I think the value currently hardcoded in the Simple Google Analytics extension is from a legacy mechanism. Nowadays, the value should be set to a value corresponding to the conversion type - these are generated ids that you can see in the code snippet adwords itself generates for each type.
My site is recording conversions, and I was inclined to believe the numbers. However, despite some debate and the above-mentioned check with the experts, Google were insistent that the value "purchase" is not valid and that the conversion numbers currently reported in my adwords account are not to be trusted.
I am going to hardcode the appropriate ID in my own copy of the add-in, but I thought I should raise this here. If you want, I can forward the email chain privately. It sounds like the add-in needs a configuration option to set the label.
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