I'll try to explain..hope it won't get confusing..
You can record in a number of ways
1. With outboard guitar effects (effect pedals) - and hear the effects as it is with direct monitoring. But most don't do this way, as it will be impossible to change the effect once recorded.
2. Use software effect : clean guitar input -> record into track as clean signal -> at the same time apply software effects (Guitar rig for example) -> audio output (with effects) back to the audio interface -> none direct (software) monitoring.
This option may have some latency - depending how good the driver and how powerful your system. If the latency is high, you can also try option 3.
3. You can split the clean guitar sound into 2 outputs, say with a small mixer with left/right output. One output goes to outboard gear and goes into a guitar amp for direct monitoring. The other output goes into your audio interface for recording clean guitar sound (where you apply effects later during mixing).
The Alesis can handle any of these above.. but I'm not sure about option 2.. if the latency is low enough for software monitoring - when I was using mine, it's mostly midi keyboards.. I'll try to setup the mixer and see if the software latency is good with guitar rig. With my Roland Quad, option 2 is not a problem - latency is low and good.