You will face a race condition, of sorts, so the outcome is unpredictable. When you download a file from S3, you might be connected to multiple S3 servers. If at any time, you request part of an S3 object and the server you are connected to thinks the object has been deleted then your download will fail.
Here's a simple test: store a 2GB flle in S3, then download it. While it it is downloading, go into the S3 console and delete the object. You will find that your download fails (with NoSuchKey) because the specified key no longer exists.
Create a temporary 2GB file and upload it to S3:
mkfile -n 2g 2gb.dat
$ aws s3 cp 2gb.dat s3://mybucket
upload: ./2gb.dat to s3://mybucket/2gb.dat
Once complete, start downloading the file:
$ aws s3 cp s3://mybucket/2gb.dat fred.dat
Completed 162.2 MiB/2.0 GiB (46.9 MiB/s) with 1 file(s) remaining
Then jump over to the S3 console and delete 2gb.dat, and this will happen:
$ aws s3 cp s3://mybucket/2gb.dat fred.dat
download failed: s3://mybucket/2gb.dat to ./fred.dat An error occurred
(NoSuchKey) when calling the GetObject operation: The specified key does not exist.