The biggest problem is usually the "gain stages"(IC:s, Transistors).
In this particular circuit you would probably need to switch some resistors to get the proper voltages on Collector and Base. If you dont you would likely destroy the transistors, or the circuit wouldnt work as it should.
I don't try my circuits with 18V unless it says they can handle it.
Check the voltage rating of your caps, and the IC. If the caps are rated at (I would recommend) 25V minimum then they will be ok. Some ICs aren't suitable but most of the common ones we use are so you'll just have to check the datasheets for any you want to experiment with. You may see some ICs are rated for +/- 12V, and these should be ok, because that rating equates to a 24V swing which makes them suitable for circuits running at 0 to 18V.
Any idea why he would want to run it at 18V Vick? seems a bit of a strange one to me - some circuits I can understand the benefits of increased voltage, but not this one. I can find no mention anywhere on t'internet of any mention of using 18V for this.
this pedal is for sale in a shop and they accidentally grabbed an 18volt power supply when a customer tried it. He liked the sound and claimed "with the 18V the pedal got a lot brighter and Fender sounding"
Personally I have no idea I do not own a 18 volt power supply.
You can usually use the same resistor for both 9V and 18V, but the led will shine a little brighter at 18V, which may or may not be noticeable.
Here's the recipe:
A standard red led will drop around 2V from the anode to the cathode (this number is called Vf). That means there will be 7V left to provide current to run the led. If the resistor is R=2k2, then the current I through the led will be I=V/R=7/2200=3.2mA. The maximum current (Imax) through a standard red led is about 20mA.
Now switch to 18V: V=16V, so I=7.3mA. Well within allowable limits. To reach 20mA with this led and resistor you'd need a 46V DC supply.
The Vf and Imax of different leds depends on the specs (color matters, standard vs. ultra-bright matters, size usually doesn't matter). You can get a general idea from google even if you don't know the manufacturer or part number.
2k2 is a big enough current limiting resistor that you should be fine for any reasonable led. The only reason to adjust the resistor is if you want more or less brightness.