... but I really wanted to use this effect while I was recording, listening to the effect and recording at the same time.
No can do - and this is quite deliberate. Here's the rationale:
The moment you record a track with any effect at all added, you never get the chance to alter this if you need to. Accordingly, the basic principle is that you record everything flat, and apply the effects afterawrds, retaining full control over the sound.
I realise that a lot of guitarists especially think that this is a bit weird - as often it is the effect that they are actually using to define the 'correct' sound of the guitar in the first place. But even so, the principle remains good - and that's why Audition lets you
monitor the track with effects added, but only records what's going in - if you want to add those effects again afterwards, that's fine, and you can add them in a controlled fashion. It even works as a principle with external stomp-box type effects - you record flat, and then re-apply the flat recording to the effects chain, and record that separately. There are two ways to do this, and one requires a multi-input soundcard; you simply record the flat signal DI'ed straight from the guitar on one track, and the effects output on another. But it's only worth doing this if you are
ultra-confident about the sound you will finally want - the safest and most flexible option is still to record flat, and reapply the flat signal to the external effects when the rest of the tracks are established, and a basic mix is in place.
This has long been the way it's done in pro studios - and it's
not just so that DI box manufacturers can sell more boxes, however much you might think to the contrary!
The other reason that it's not a good idea is based on the problem that you are running into. Effects are often processor-hungry, and clearly what is most important is making an intact recording. This is especially the case with a multiple-input session using a lot of separate tracks - the last thing your PC needs whilst doing this is a heavy extra processor load caused by adding effects. So, what is desirable from a mix perspective is also desirable as far as the PC is concerned - quite conveniently for a change...
Even basic studio reverb, in the context of trying to record simultaneously, is clearly adding enough extra load to cause problems - it really doesn't take too much of this under these circumstances.
If you have enough processing power, a multi-input soundcard, and really are desperate to record the effects at the same time as making the original recording, you
can do this - but the only way is to physically route the monitor output back to another pair of inputs, and record this as well. There will inevitably be latency, so you would have to shift the effected track forwards in time after you'd recorded it anyway. Generally, it simply isn't worth the hassle.