ttsce - really brief - for Inmarsat satellite frequencies the answer is "some" but not dramatically. The antenna tracking test for Inmarsat-M antennas was suited for a ship in very rough weather that would normally include a deluge. And that's in the same band as the new stuff
Ships have no or little limitations in terms of space, weight or aeodynamics.
There is no comparison between a 20dB+ parabolic antenna (with tracking) on a ship and an a/c planar omnidirectional antenna.
So they do specifically state which satellite was in use and that basically puts them almost dead center under it. It would take something fairly dramatic for them to lose the satellite. A 30 degree or so change in attitude that was not corrected by the antenna steering logic could do it.
Steering logic ? are you sure Aero-L antennas (L band !) have tracking capabilities ?
Dead center or not does not make a difference, be it 35,800 or 37,000km, same thing.
Point is, the link is not 100% guaranteed, and while L band is a lot less sensitive to precipitations or proximity to the core of a storm than eg. Ku band, it still is not immune.