When Accuracast questioned Google, the response they got from a Google Adwords account manager not only confirms this, it even suggests that disabling images on a phone browser can prevent tracking Adword conversion:
A significant percentage of mobile browser and carrier combinations do not support cookies. Google adds cookies to a user’s mobile device when he or she clicks on an ad to track conversions. Therefore, if users are using mobile browsers or carriers that do not accept or support cookies, they will not be included in your conversion tracking statistics.
Additionally, cookies on mobile phones expire faster than the ones created for PCs. Therefore, a significant number of conversions for your site may go unrecorded after a certain period of time. When viewing conversions for a specified time period, note that conversions are assigned to the date on which the ad click occurs, not the date on which the conversion occurs. In addition, we will not be able to report conversions for users who disable cookies.
Conversion tracking is also not supported when users disable images on their mobile phones.
Although Google cannot record every conversion due to the reasons mentioned above, your conversion rate, cost-per-conversion, cost-per-transaction and value/click are adjusted to reflect only those sites from which we can track conversions.
I am also surprised that this is not bigger news.