I'm working on a project (non-Arduino) where I need an indicator light to know if a 120VAC heater element is on. I've found several examples online of such a circuit, but would something like this be sufficient?

Don't use the resistor, use a 0.1uF (rated 200V or more) capacitor instead and nothing gets hot.
Amazing.
XC = 1 / (2 * pi * f * C) = 26k?, you'll get about 4ma.
hmm, cool. That sounds simple enough. I will see what I parts I have in the junk bin. Do I still need a reverse diode as in the above diagram?
Do I still need a reverse diode as in the above diagram?
Yes. Telephone circuit have them, because of the high AC ringing voltage. Instead of a LED, an opto-coupler is being use as a ring detector. It also use a two 24 V zener diode.
Connect like : Hi V cap --- Hi power R ----- C -- A ----- A -- C --- A - C -
--A - C -
Don't use just a capacitor, it will put a large surge through the LED when you power it up. Use a resistor in series with a capacitor. Choose the resistor to limit the surge (e.g. 4k7 will limit the surge to around 30mA on a 120VAC supply) and the capacitor to get the right current for the brightness you want (e.g. 0.1uF 200VAC for 4mA as already suggested).
Although a power diode such as the 1N4004 will be OK in this circuit, a small signal diode such as 1N4148 will suffice.