I don't believe Audacity will check peaks for you. And yes, hitting 1.0/-1.0 on Audacity's scale is clipping. You can change the scale to DB, if you wish. Notes on this, and more, here:
http://taperssection.com/index.php/topic,71191.0.html.
As you've already found, you could adjust the volume in the quiet sections using the Amplify function, but that would result in sudden increases/reductions in volume, and wouldn't sound very good -- no transition, just an instantenous gain change.
The goal with the volume envelope is to adjust the volume in a flexible way for the quiet section(s)
only, and to not adjust the volume of the rest of the recording. When you first turn on the volume envelope, the yellow line comes in at a baseline of 0 dB, i.e. no gain change.
I've attached an Audacity screenshot to illusrate the flexibility of the volume envelope. As you can see in the first gain change in the attached image, the volume envelope will allow you to add all the gain, all at once -- just like using the Amplify function. This results in a squared off transition. Very distracting during listening. The volume envelope also allows you to control the slope of the gain change. See the 2nd example -- it's not a vertical transition from no gain to full gain, like in the first example. Instead, it's a more gradual, but still linear, transition. This may suit your purposes, it may not -- play around, use your ears, decide if you like how it sounds. Finally, the 3rd example shows an example of a curved transition. You can apply a single curve, controlling which way the curve bends. You might opt to use two curves, like more of a sine wave. Up to you. Note: I didn't apply the volume envelope in these examples for listening -- they're strictly a visual aid. The actual volume envelope slope / curve may (will) be different for your application.
You may have to play around with it a fair amount to get the transition(s) the way you like. But it can be done. It won't work wonders, but it may make the recording more listenable without having to reach for the volume knob during playback. And remember, less is more. The goal (IMO) is not to raise the level of the quiet sections so they're equal to the loud sections, but to simply reduce the difference in volume between the loud and quiet sections.
Alternatively, instead of making the quiet sections louder, you could reduce the volume of the loud sections. The volume envelope will do this -- just imagine the attached screenshot, but with all the volume envelope points inverted. But there's not much point in using the volume envelope to reduce the volume of the loud sections. Instead, you could try compression. Compression will reduce the difference in volume between the loud and quiet sections. Links to info on compression here:
http://taperssection.com/index.php/topic,117279.0.html.