If there's food, they'll stay. Migrating is a hazard, if they don't have to, they won't.
Not necessarily true in this part of the world - Fieldfare is overwhelmingly a summer visitor (widespread and common), relatively small numbers winter each year (odd ones here and there, small flocks). Overall, I can't say there seems to be appreciable differences in the numbers when there are good berry crops versus poor berry crops. This said, if you find berries in winter, it often concentrates the remaining Fieldfares, so will certainly provide you with overwintering birds, just don't think it actually affects overall total numbers wintering very much.
Even if good, the berry crop is unlikely to be sufficient to last all winter and when snow coats the ground and sub-zero freezes all, there is precious little other food source to support large numbers, so would seem prudent that most migrate beforehand anyhow.