No, unmodified non-segwit miners will be producing valid blocks and their blocks will still be accepted. Segwit transactions are considered by non-segwit nodes as being non-standard. An unmodified non-segwit miner means that they have not changed any of the local node policy rules, which include the standardness rules. As long as they are following the standardness rules, they will not be mining segwit transactions and thus their blocks will not be invalid. These miners will not have their blocks orphaned unless they mine a segwit transaction, but that will only happen if they modify their standardness rules.