Is it ok to have a power inverter draw more watts than the battery has?

I have a 12v 18 ah battery and I'm expecting to run it for about 3 hrs so then that is 72w coming from the battery, correct? Ok then I have a 200w continues power ac to dc inverter so is it ok to hook them up and can i charge something like an iPhone.

The energy stored in your battery is measured in watthours, not watts. In your case your fully charged battery in good condition would hold 12*18 or 206 watthours. Watts would be the rate that you use that energy. If your inverter was fully loaded to its 200 watt continuous capability, the battery would last about an hour.

As it is modern inverters are very efficient circuits and only use a small amount of power for themselves while the rest is available for the load, in this case your iPhone. You phone only uses a small percentage of the power available. The rest of the inverter's capability is not used and as a result it only draws a small amount of power from the battery.

Based on hundreds of inverters that I've worked on, I'd estimate that rate of energy use by your lightly loaded 200 watt inverter to operate its own circuitry to be no more than about 5 watts and your phone charger might use another 5 watts at most.

Your fully charged battery should be able to power both for at least 20 hours.

No, as you shorten the life of the battery.

But a 200W inverter is capable of powering a near 200W load. It does not draw 200W no matter what.
It draws what the load draws, plus a bit to run itself. A bit is lost as heat.

Your charger draws a dozen or so watts. You might draw 20 watts from the battery. That should charge/power your phone for a few hours.

You will lose less power using a car charger directly from the battery.