Should the overall level of the tracks hit between +4 and +8 on the stereo VU meter having the volume level set at unity? Would this make the compression process bring out the bottom so much that it would sound distorted?

This is quite a question, actually.  Increasing the level going into a compressor can increase sustain in the bottom range, causing low frequencies (which have more energy) to break up at different points.  (High frequencies have more intensity, and can cause different issues as well.) 

What to know: A standard VU meter only displays up to +3 VU, but the amount of voltage of the actual electronic signal  that the meter is displaying is different than the VU meter's numeric scale.  "+4" is "line level" which equals about 1.23 volts (+8 output level would be a non-standard voltage).  Typically, line level should be represented by a meter reading of "0VU" in a common signal path in the hardware world.  See, VU meters were designed to "look" like the sound you hear, and often they were paired up with analog tape.  But the trick is that tape actually has 14 dB of headroom above the calibrated standard "0" VU meter display!   The "bonus" area of +1 +2 and +3 on a VU meter really is just the beginning of the headroom that's supposed to be there for the purpose of avoiding distortion. 

Often we think back to the days of slamming meters when recording to analog tape.   Slamming the signal going to analog tape (meter's-a-peggin') used to be cool (remember there was actually 11 dB more invisible headroom above the VU meter's scale) but those pesky red clipping lights on a Full Scale digital meter (peak) is definitely NOT cool because there is no "bonus" room above clipping!  Those red lights don't sound good the way analog pegging sounded!  Don't look at them the same way you look at a VU meter. 

Digital meters show you a different picture that is Full Scale, meaning there is NO headroom above the top.  None.  Full scale meters show you the peaks with no averaging (unless it's a Dorrough meter).  For instance, a triangle or other small percussion instrument can "light up" a digital peak meter all the way, but hardly move the needle on an analog meter.  We recommend at least 2 dB of headroom before clipping an digital meter.  The main reason you don't see VU meters on digital audio workstations is because the software company doesn't know how you are going to calibrate your D-A converters which determine how much electronic signal strength you're putting out. 

Metering and gain structure is important at all stages to avoid distortion. Unity gain is really a point in hardware gear where the calibrated signal in equals the same calibrated signal out.  Digital virtual consoles and plug ins often operate the same way, but distortion occurs at different points in different systems.  Calibrating digital systems (with a smooth sine wave test tone) starts at  -18dBFS which has been a "standard" reference point (18dB below full clipping).  However it gets confusing when it comes to audio CDs, which have gotten louder (a more elevated level) and so sometimes the D-A converter output needs to be changed to accommodate a hotter signal that could cause distortion.

Unity gain is where the signal is supposed to be ideal, or at least it's a place where you have room above and below the signal to get great sound and less noise.  See your instruction manuals to get more info about your gear and how it's best set up, and above all, use your ears.. carefully!