Hi there,
It is possible to upgrade on select routes, but this is basically never a good deal. As the JR Pass would only cover the base fare, and you'd have to pay for the high speed fare + Green Class fare separately.
Let's break this down further, in Japan a total fare has different components:
1.) Base fare, simply based on distance travelled
2.) High speed fare: charged for fast trains, such as ltd. express trains and Shinkansen
3.) Green Fare, for first class seats
(+ optional seat reservation fee).
The JR Pass normally covers all these, and the Green fare when you have a Green Pass. That's one reason the JR Pass is such a nice thing, you don't even have to think about these things, but let's not get side tracked.
For example Tokyo - Kyoto:
Distance fare: ¥8,360
High speed fare: ¥5,810
Green Fare: ¥4,870
Total: ¥19,040
If you wanted to upgrade this fare with a normal JR Pass, then the cost would be high speed fare + Green fare ¥10,680, as the base fare would be covered. The price difference between a normal 7-day JR Pass (¥29,650) and 7-day JR Pass Green (¥39,600) is ¥9,950 yen. So you'd have been better off just getting a Green Pass from the start.
I hope you find this useful,
Daniel