What you describe is ruled out by ECMA-262. The maximum value that can be returned by Date.now is ±8.64e15, which is well within the range of integers safely supported by ECMAScript.
The maximum value can represent 1e9 days either side of the epoch (1 Jan 1970) so a range of approximately ±273,790 years. I think there will be time to address the issue before it arises.
Constructing a date for the maximum value returns a date for +275760-09-13T00:00:00.000Z. Adding one millisecond to the time value returns an invalid date:
// Max value returnable by Date.now
let maxDateNowValue = 8.64e15;
console.log(new Date(maxDateNowValue).toISOString()); // +275760-09-13T00:00:00.000Z
// Max value plus 1 millisecond
let plusOneMS = maxDateNowValue + 1;
console.log(new Date(plusOneMS).toString()); // Invalid Date