We investigate whether Alfvénic fluctuations (AFs) can affect the structure of magnetic ejecta (ME) within interplanetary coronal mass ejections (ICMEs). We study an ICME observed on 2001 December 29 at 1 au by the Advanced Composition Explorer (ACE) and Wind, at a total angular separation of ~08 (~ 0.014 au). We focus on the correlation and complexity of its magnetic structure measured between two spacecraft in association with large-amplitude AFs. The Alfvénicity of the ME is investigated in terms of the residual energy and cross helicity of fluctuations. We find that as for the event of interest, large-amplitude AFs occur in the rear region of the ME at both Wind and ACE with a duration of about 6 hr. We compare the correlation of the magnetic field strength and vector components measured between Wind and ACE, and investigate complexity in terms of the magnetic hodograms. The region showing AFs is found to be associated with a decreased correlation of the magnetic field components and an increased complexity of the ME magnetic configuration detected at ACE and Wind, which may be due to the fact that the two spacecraft crossing the same ME along different trajectories likely sampled AFs in different oscillation phases. Combining multipoint in situ measurements and remote-sensing observations of the ICME source region, we further discuss different potential sources of the AFs.