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One quick remark:

if (N === 0) return true;

can be replaced by

if (N <= 1) return true;

because in a non-empty array each element is a single "consecutive number." This saves the sorting of the array in the case \$ N = 1 \$.

Some quick remarks:

if (N === 0) return true;

can be replaced by

if (N <= 1) return true;

because in a non-empty array each element is a single "consecutive number." This saves the sorting of the array in the case \$ N = 1 \$.

Then it suffices to check the count again only if it has been incremented.

The comparison with the previous number (or null) can be simplified slightly.

 for (const num of sortedArray) {
 if (prev === num - 1) {
 count++;
 if (count === N) return true;
 } else {
 count = 1;
 }
 prev = num;
 }

(Inadvertently hit the post button :)

One quick remark:

if (N === 0) return true;

can be replaced by

if (N <= 1) return true;

because in a non-empty array each element is a single "consecutive number." This saves the sorting of the array in the case \$ N = 1 \$.