Logic Studio 9 : Is it possible to use tracks or buses as "virtual devices"
If Skype supported the ReWire protocol directly this would be no problem at all. You'd wire Skype's output to Logic 9, run it through your effects, and then wire the output from Logic 9 to Skype's input. But Skype doesn't support ReWire.

So instead you have to hijack it's audio input stream and feed it a stream from Logic 9. To do that you can use the most awesome SoundFlower app from the great folks at Cycling '74. It's free!

SoundFlower presents itself as an audio device to your computer. Except its only use is to route audio between applications. The 2ch mode is what you'll need to accomplish your goal here.

You'll set Skype's audio (microphone) input to be SoundFlower's output -- lets say the left channel output.

In Logic you'd create a new Audio track that takes its input from from the built-in microphone on your Mac. To enable the internal mic in Logic go to Preferences -> Audio and under the Devices tab select the Core Audio sub-tab and pick 'Built-in Microphone' for device.

Create a new Logic project. Add a new, mono Audio Track with the input coming from the internal microphone. Connect output of the track to the SoundFlower input channel. Pile on whatever effects you'd like on the channel (no real need to use a sub-mix buss in Logic here). Watch the levels in Logic and Skype and adjust to taste.

There's going to be some latency involved in all of this. And whether your third party will pick up on that or not depends on how big the latency gets as you pile on effects.