Users (in this case drivers) are creatures of habit. They will generally drive the same route to and from work. After so many trips along these routes (home to work and work to home), they will have their surroundings mapped in their head (pattern recognition). If any change occurs, they are more likely to notice it because it will stand out from what's been mapped in their head. Of course, after a while, this new sign will be mapped in their head too and will stand out less.
This is true of a gas station switching from physical card numbers to digital numbers or even vice versa. Now light itself is more attention-grabbing than physical cards, so in the context of switching from cards to digital numbers a brighter light is being added and will grab their attention more. In the opposite context of switching from digital to cards, light is removed and so it may appear like something is missing rather than added (due to the shift to a less attention-grabbing medium).
Now since light is more attention-grabbing, the new digital number display will grab their attention, and it obviously specifically calls out the prices. However, whether or not it turns into a sale is dependent on the price itself and if they need gas. In marketing, the goal is to get the customers attention, inform them of what the product is, and convince them to buy it. In this case, the user's attention has been grabbed.
If the user notices the new display and notices that they are low on gas then they are more likely to get gas. But do they get it there or down the road at the next stop?
Side note: Just because the sign is more attention-grabbing does not guarantee they will see it. They may be oblivious to their surroundings due to texting while driving, or are more focused on the road like a good driver, or just dodged an accident, etc.)
So if they notice the new display and see that the price is higher (due to some shortage, oil spill, political climate, high-demand season... basically supply/demand and/or greed) then chances are the pricing and their need for gas will be the biggest factor to whether they buy or not. Upon seeing the price, some users will think to buy gas before it goes up even more while others will wait and see if it goes down. This behavior is regardless of if they noticed the price more or not. There are too many variables at play with the price of gas and the behavior of a user based on that. In contrast, if the price drops significantly, it could very well increase sales.
I think the real question here is how pricing (and rapid or slow rates of change) affects sales. You'd have to look into research surrounding that question.
TLDR: The digital sign may have their attention, but pricing and their own need for gas is the largest factor to convert this sale.