I also take a pre-workout before exercise sometimes, but ONLY in the morning. I may take a little Amino Energy that late in the day but that is 50-100mg, but I am usually pretty strict about no caffeine past 1-2 PM with a usual 9-10pm bedtime.
You may be able to fall asleep ok with that dose, but internally your sleep quality is going to suffer. Same goes for Melatonin, sleep aids, etc. They may help you fall asleep, but they will not keep you asleep or help you achieve that DEEP REM sleep that your body needs for true recovery.
I would try and ditch the caffeine that late in the day and save those workouts for your easy/Zone 1/2 workouts.
My .02