You know, theoretically you could just use ammonia absorbers all the time; the result you want whether using ammonia absorbers or cycling the tank is the lack of nitrogenous waste. I've kinda pondered this one from time to time...what I've decided is its better to have the tank cycled. One can never be sure when the ammonia absorbers are "full" without constant testing; testing is still needed with cycling but on a weekly or biweekly basis...I would think it would be required more often with the absorbers. Then if there is an ammonia spike there is nothing to remove it (even tho a spike in a cycled can happen, the bacteria can work on it) and you'll need to add more or recharge it (assuming you are available to do that). Plus, some ammonia absorbers can be recharged with salt; one of the folks here discovered using salt in the tank can cause the absorbers to discharge the ammonia. Lastly, ammonia absorbers only remove ammonia, and not nitrite/nitrates so far as I know.
Oh and just to clarify, testing is always necessary
aka Cycling Guru and the Ich Slayer
*glares at Terry and QTOFFER*
Card carrying member of FTAS & GCAS.