Interesting question. If what they're putting on the translator does not appear on - air >somewhere<, they might have a problem.
That *is* an interesting question.
The rules for translators of *AM* stations allow the translator to operate if the AM has operated in the last 24 hours. I would *suspect* the FCC would interpret it the same way for translators of HD2/HD3/HD4 -- that if the HD is off for more then 24 hours the translator must shut down -- but that's only a wild guess, nobody really knows what the Commission would actually do.
However, many translators - mostly religuous - are fed via satellite. Thus they'd only need to put it on one of their other stations someplace, and if it's syndicated, they likely are.
But you can only do that with non-commercial stations. Translators of commercial stations, if they receive financial support from the primary station (or are owned by the primary station!) must be located within the theoretical coverage area of the primary station.