I have heard of this.....but I think the possible old oil that new oil would "push out" would be very mininal...
I could see if the vehicle took 4.5 quarts, and you buy the 5 qt jugs, sure you have a half quart "extra" essentially....I could justify adding that....but I think the benefits would be minimal...
If you're that worried, better off taking a couple low mileage back to back OCIs....i.e.: 1500 mile oil and filter change, back to back...if you were really concerned of "mixing" say a conventional oil, with a esther-oil/synthetic on a "which over" from conventional to synthetic.
Or [censored], in the aforementioned example with the 4.5 quarts, I'd be more likely to SAVE that 1/2 quart, and empty the filter say 1500 miles into the OCI, then top off with all/part (based on dipstick level) of that 1/2 remaining quart....
Would seem more justifiable to empty the filter, than try "pushing" old oil through the drain hole with "virgin" oil
Or, [censored], just save the 1/2 quart of oil, and use it for the off chance that you need a top off....
You get the jist, lol. But no, I can't see dumping new oil down the fill hole, in hopes of pushing out the old oil....