Can an inductor/capacitor/resistor combo emit the same frequency as a given crystal oscillator?
Yes, you can build a oscillator with inductors and capacitors that will have the same frequency as your crystal oscillator. Using inductors and capacitors, you can reach frequencies much higher or much lower than you can reach with crystal oscillator.

The reason why crystal oscillators are used is because they have a much better frequency stability. Frequency stability does not matter much for an experimental DIY toy FM transmitter, but it does matter for many other uses.