Is it ok to represent dates as Unix time (seconds since the epoch) in JSON?

Yes.

If your JSON contains integer numbers that represent Unix time (seconds since the "epoch"), and you parse your JSON to JavaScript, the range of integers that can accurately be represented is -9007199254740992 to 9007199254740992 (ref: EcmaScript standard, section 8.5).

The year 4000AD starts at unix time 64060588815, which is 9007135194152192 less than the maximum.

The year 1AD started at unix time -2177452800, which is 9007197077288192 more than the minimum.

So there are enough numbers.