No, SRAM grip shifters will not work with a Shimano road derailleur.
The SRAM 11 speed grip shift units I found online use what SRAM calls x-Actuation which means a derailleur actuation ratio (length cable pulled to derailleur movement) of 1:1.12. Shimano 11 speed road uses 1:1.4.
Source for this info: https://www.artscyclery.com/science-behind-the-magic/science-behind-the-magic-drivetrain-compatibility/.
However, I think you probably have deeper compatibility issues that I should point out. If your bike is vintage then is will have narrower hub width than modern bikes, 120 or 126mm perhaps vs 130 or 135mm. An 11 speed cassette will not fit on a narrow hub which makes me think you actually have a lower speed bike. As the number of sprockets increases the spacing decreases, therefore you cannot use a 11 speed derailleur/shifter combination on a sprocket cluster with less than 11 sprockets, as the sprocket spacing will be wrong.
The basic rule of derailleur and shifter compatibility is the shifter speeds need to match the number of sprockets, and the derailleur needs to match the actuation ratio the shifter expects.