Rescaling logistic regression predictions for under-sampled data?

I'm building a predictive model for a large dataset with a binary 0/1 outcome that is heavily imbalanced.

I'm under-sampling records from the majority outcome class (the 0s) in order to fit the data into my computer's memory prior to fitting a logistic regression model.

Because of the under-sampling, do I need to rescale the model's probability predictions when choosing the optimal threshold or is the scale arbitrary?