Winterlong, the above posts are right. Growth happens during rest. I'll give an extreme but personal example.
In 1993 I was drastically overweight and was 34 yrs old. I worked constantly, never took time off and ate for energy. At 6', I weighed 385. I joined the gym, and 6 days a week I did 45 min of weights with a split routine-hitting each bodypart twice a week, followed by an hour of varied aerobic work. I did the low fat thing back then as well.
After 12 months I weighed 250, and my 48" gut had went down to 38" I then decided to up the protien, up the rest, and lower the carbs just a bit to see if I could put on some muscle and strength-two things that are hard to do, when losing weight rapidly and training like I did.
In the next 6 months, training 3-4 times per week and dropping the aerobics to 20 minute sessions, I made the best gains of my life. Upper Arms went to 19.5, chest went to 59" waist was 34" thighs were 30", and calves went to 20". Gains continued, but that 1st 6 month period was a quantum leap. Hell, I was doing seated barbell behind the neck for a top pyramid set of 3 reps with 315. I was also lifetime natural.
This is an example of what a formerly overtrained body can do once it's had a chance to recouperate.
If your goal is to work out alot-go ahead. If your goal is to make the best gains you can in the shortest amount of time, back off to a more balanced approach.