The "Nitrification Processes" on a whole is a delicate balance of many factors...ammount of nitrosomas bacteria, nitrobactor bacteria, waterflow,oxygen levels-oxic-suboxic-anaerobic,surface area,nutrients present for each type and level of bacteria...
In a well established tank these levels are almost self regulating and are able to increase and decrease to small changes as they occur in the tank...the cycling process is still/constantly going on, you just won't see any "measurable" changes other than maybe nitrAtes going up.
In a "New tank" these levels are out of "balance" and "measurable' amounts of ammonia,nitrIte,etc allow us to "chart" the progress of the cycle and determine when the tank is "safe' for inhabitants...which when added changes the balance of "nutrients to bacteria" and can cause a "mini cycle"/measurable changes...until the tank becomes "established" with large amounts of LR/LS (surface area for bacteria) good water flow (oxygen) and clean up crews (to "preproccess waste) at which point it becomes "self regulating"
Moving large amounts of this "established rock/sand to a new tank will help jump start the process of "becoming a established/balanced" system, but the inherent changes from disturbing the sand bed (mixing oxic-suboxic and anaerobic zones) as well as the change of nutrient levels in the water column will still need to readjust to "maintain" colonies of bacteria at self sustaining levels.( the imbalances will work themselves out,mini- cycle)Whether or not these reach "measurable" amounts.
So YES, it is possible to NOT have a "major/harsh" cycle in a new tank, (control the cycle) with the addition of LR/LS/bacterial boosters...as well as experience a "cycle" in moving an established tank.
It all depends on how 'close" to a balanced self regulating level of "biological filtration" you have in your tank.