classification feature selection
You have a problem of data leakage.
The "days since invitation was sent" feature contains all the information on the concept. Therefore, adding it as a feature will prevent most common classifiers from using rules based on other features and will lead to misleading results.

Duplicating the negative row for each predefined time value will lead to a different distribution than the one you should be tested one, which need needles problems. 

Note that even that way, the feature might leak information (e.g., a small ratio of the positives will replay in two weeks while its distribution in the negatives will be higher, making it a good predicator for negative).

In case that you will have more complex representation of time (e.g., was the email sent on weekend? was the reply sent on weekend), the duplication of rows will be more complex.

I would try a different direction. It is likely that the negative rows has no influence on the time to reply in the positive ones. 
Therefore I would do a first research aimed to differ between replies and no replies without using the predefined time.

After that, do a second research only on the positives where the concept will be the predefined time, aiming to find what is influencing out given that the user had replied.