Most miners move to coins where it's profitable to mine, so I'd guess they switch (assuming you buy the premise that tx fees alone will not be able to fund a safe, decentralized blockchain, and one person or company's going to swoop in and threaten the coin they're mining by capturing 90% of hashpower). Whether or not they use the coins they mine or use one of the auto-converting pools where the coins are automatically traded to BTC which they'd then use for actual transactions is hard to say, and probably heavily dependent on the fungibility and merchant adoption of the coins.