You should also be aware that the situation is not necessarily binary, i.e., pattern or no-pattern. Depending on the interaction, the result can be any of the continuous set of possibilities between a clear interference pattern and no signs of any interference at all.
Let's take an extreme scenario of a detector that can be in three states: 0 - default, L - the particle went through the left slit, R - the particle went through the right slit. Let' assume that the detector is perfect, i.e., starting from the state 0 it always changes to either L or R depending on the interaction with the particle. Immediately after going to the L or to the R state, the detector self-destructs. Then, another such detector interacts with the next particle. And so on.
There will be no interference pattern in this scenario.