If I sell an American style ITM covered call, then in theory, can I get an assignment notice as soon as I have sold the call, since the counterparty can opt for early exercise? Does this ever happen or do I get the assignment notice only upon expiry?
Yes, in principle this can happen, although you usually only get the notice the day after the option was exercised, due to the assignment process. In practice, however, the only time an early exercise may make sense is just before the ex-dividend day. In all other cases it is better to sell the option again instead of exercising it.