It might affect the tone, or it might not be noticeable.
The 1N5817 diode in this circuit (and a lot of the circuits posted here) is used in series with the DC input. If power is accidentally applied the reverse way, the diode will stop it so that it doesn't damage other components in the circuit. Check the schematic and it should make sense.
A diode in this position drops the voltage coming into the circuit. A 1N5817 has a very low forward voltage, so it doesn't drop it very much. (probably around 0.2~0.3V I'm guessing in this circuit). A 1N400x has a higher forward voltage (maybe around 0.7V in this circuit). So, using a 1N400x in this spot will give you less voltage on your op amp.
Having a lower voltage on the op amp could cause the op amp to start clipping sooner, which is a harsher distortion than the diodes provide. I don't if op amp clipping happens this circuit, but they use a special op amp (OP2134), so that makes me think maybe it does. Also, the clipping arrangement (3x 1N914 vs 2x 1N914) is a higher clipping threshold than many pedals, which makes it more likely for the op amp clipping to contribute to the sound.
You have a few options.
-Put in a 1N4007 and not worry about it.
-Put a jumper instead of a diode so there is no voltage drop (be careful to never run it with the wrong power).
-Install a socket so you can try different diodes and see for yourself, or so you can get the pedal working with a 1n4007 or jumper for now and replace it with a 1N5817 later.
-Run the pedal at 12V or 18V. Then your starting voltage is higher anyway so dropping it by a 1N4007 is no big deal. Just make sure your electrolytic caps are rated for more than the voltage you run it at.