Yes, but with lower intensity. There is alot involved in the body's recovery process that goes beyond just recovery of the muscle fibers and energy reserves. You still have to consider the recovery of your hormonal system and central nervous system.
If you constantly beat yourself into the ground with super-intense workouts, you will not allow the body to recover fully ... then your gains stop ... then you're overtrained. No good.
The way around this is to cycle your intensity: Have most days be work days where intensity is high, but not to the point of all-out exhaustion.
Every once in a while (I like to do it every 2 weeks or so), go all out and try for personal bests in ALL of your lifts. Go for that 10 lb. increase in chest presses ... Try to nail that heavy squat that you know is JUST beyond your reach ... Of course, be sure to have a spotter around to help you.
Once per week, and always after an "all out" day, do a light workout where you go lighter than usual, but use REALLY REALLY strict form through a full range of motion and focus on contracting (squeezing) the muscle you are working (for example, when you do a biceps curl curl the weight up for 3 seconds, flex your biceps when the weight is in the "up" position, and then lower the weight.