Convective rolls contribute largely to the exchange of momentum, sensible heat and moisture in the boundary layer. They have been shown to reinforce air-sea interaction under strong wind conditions. This raises the question of how surface turbulent fluxes can, in turn, affect the rolls. Representing the air-sea exchanges during extreme wind conditions is a major challenge in weather prediction and can lead to large uncertainties in surface wind speed. The sensitivity of rolls to different representations of surface fluxes is investigated using Large Eddy Simulations. The study focuses on the Mediterranean windstorm Adrian, where convective rolls resulting from thermal and dynamical instabilities are responsible for the transport of strong winds to the surface. Considering sea spray in the parameterization of surface fluxes significantly influences roll morphology. Sea spray increases heat fluxes and favors convection. With this more pronounced thermal instability, the rolls are 30\% narrower and extend over a greater height, and the downward transport of momentum is intensified by 40\%, resulting in higher wind speeds at the surface. Convective rolls vanish within a few minutes in the absence of momentum fluxes, which maintain the wind shear necessary for their organization. They also quickly weaken without sensible heat fluxes, which feed the thermal instability required for their development, while latent heat fluxes play minor role. These findings emphasize the necessity of precisely representing the processes occurring at the air-sea interface, as they not only affect the thermodynamic surface conditions but also the vertical transport of momentum within the windstorm.