Inverse FFT of complex exponential with time delay - window leakage?
Yes, this is leakage.

Your problem is in the discrete domain and your nomenclature is for the continuous domain.  Often times the two are conflated, as you have done, and this causes confusion.

The inverse DFT and the forward DFT are basically the same animal.  The only difference is the convention used in the sign of the exponent and the normalization factors you use.  So a window function can "shape" your sidelobes (leakage) somewhat, but can't eliminate them.

What is your larger purpose?