Yes, Martingale betting systems are permitted when you play casino games online. There's no reason why it wouldn't be prohibited. In the long term, the casinos will always take money off players, but those prepared to practice Martingale for short-term bursts could succeed.
Double bets are a great way to maximise your profit potential on two outcomes that you would have probably wagered on anyway. In combining your two single bets, you increase your risk but also your odds.