Are there any drawbacks to this oscillator frequency multiplier circuit?
Complex gates are not as fast, just use an invertor.
74AC04 will run at 125MHz, and has the lowest Z of cmos. 

You can connect the unused outputs to GND and VDD to help lower the supply impedance

74Ac11004 had a nice centre power lead arrangement that made it great for this, they can deliver 200mW at 100MHz

I have used 74HC04 to triple 50 to 150MHz (before 74AC existed). To get decent power it was turned into more of an injection locked oscillator by putting a tuned circuit around it. This took it from a few mW, picking off harmonics, to ~50mW. I think it was like this - it was a very long time ago







simulate this circuit &ndash; Schematic created using CircuitLab

Of course you might find the traditional transistor multiplier uses far less power...