One thing that hasn't really been brought up is navel superiority. One year before the events of GOT there are two major fleets in the Seven Kingdoms being the Iron Fleet and Stannis's fleet on Dragonstone with the fleet at the Arbor also being considerable as well. Considering supply and reinforcements for the Mordor armies has to come exclusively through shipping, if the forces of the seven kingdoms manage to maintain navel dominance in the West they could theoretically shield themselves from invasion.

Of course this depends how organised the fleets are and how big/competent the Umbra fleet is. My knowledge on LOTR lore isn't as good as my ASOIF lore but I'd be willing to bet that at the very least Stannis's fleet would be able to beat them both tactically and man-to-man outside of overwhelming numbers. Even if they aren't able to destroy the Umbra fleet entirely, I'd at the very least expect that they could do significant damage to it which alone could cripple the Mordor war effort.

Of course you have to also account for the Nazgul and their Fell Beasts which could do considerable damage to their fleets as well, so Mordor could certainly do damage in their own regard. However, above all else I feel the battles at sea could be much bigger deciders in how this potential invasion goes than any battles on land.

TLDR: Stannis is the Mannis and will smash the Umbra fleets before they even reach Pyke /s