Oh yes they will! I just had the pleasure of experiencing this. My Sugar Mango Ryder got way taller than what I thought it was going to and I freaked after finding that my flowering tops hit the lights... Every one of them burned TO A CRISP after hitting them. My answer was to quit trying to grow something in a contraption that wasn't meant for it. The plant has since been moved to a closet and placed under an LED light. You aren't out all that money you spent for the Aerogarden however! What you now have is a fantastic machine to start your autoflowering seeds in and then transplant to a bubble bucket! It truly is the best of both worlds and it is small enough that you can place it right into the closet with the bucket plant. Two or three weeks before your flowering plant is finished just start a new one and CAREFULLY remove the root plug and bury in the clay pebbles after the flowering one has finished! A constant supply... NICE
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I know this thread is hella old but I hope that someone finds it and heeds my warning! DO NOT FULLY GROW YOUR AUTOS IN THE AEROGARDEN!!!