For HDDs, the beginning of the disk platter is the fastest and the end is the slowest. So depending on where the test file used for benching is placed, you will accordingly see a drop in speeds. So yes, the amount of empty space affects HDD bench.
HD Tach best illustrates this difference in speed across the platter :-
SSDs are a little different in their structure, but even their benchmarks are noticeably affected by the amount of free disk space.