Can a 1.8V linear regulator be avoided with 5V power and 3.3V?
No, in virtually all cases the 1.8V rail must share a ground with the 3.3V and 5V supplies so that won't work.
Even if you did have some strange load that didn't care about grounding (say an infrared LED) there's another more subtle reason- that most regulators can't sink current, so your 1.8V load would run the risk of increasing the voltage on the 3.3V supply and damaging everything connected to it.