Nope. Miners just blindly hash the header. They don't make any attempt to determine whether the "Previous Block" attribute has been used before or not.
But, one of them can realize if they're trying to reorg it. One's enough to spear the news, isn't he?
Can they? Perhaps, but it's VERY unlikely.
Reorgs happen all the time. Nobody is likely to notice a significant reorg that damages the integrity of Bitcoin until AFTER it has happened.