Is sub-sampling delay estimation possible without interpolation?
For finite length signals, interpolation (both for frequency and phase) in the frequency domain is helpful if the frequency is not at a DFT/FFT bin center.  Relative phase estimation is required for delay estimation in the frequency domain.  This relative phase estimation can produce a sub-time-domain-sample delay estimation result.  This delay estimation can have an uncertainty related to an unknown integer multiple of the signal's period due to phase unwrapping errors, unless there is some other time domain envelope information available.