If several sebaceous gland cysts burst over a small window of time, could it create a very severe seborrheic dermatitis, one rivaling cradle cap?
No. This sounds like one of those internet legends. No, if you have severe seborrheic dermatitis it is not due to sebaceous glands bursting. If it truly is "very severe", you should consult a dermatologist.
It is possible. A sebaceous cyst that ruptures is usually one that is already infected. The skin is our greatest defense against infection, once broken, no matter the source, the risk of bacterial infection is greater. Certainly location and other risk factors such as concurrent medical conditions such as diabetes make more serious infection possible. Medical attention is recommended.