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It's referring to the server side. Try taking a backup from the back-end. If it fails, please follow the following procedure.

First try upgrading to the latest version of Akeeba Backup (you can check the latest version from here.

Then try clicking the Configuration Wizard button in Akeeba Backup's Control Panel page. If the wizard hangs after the database step, try reloading the page. Try taking a new backup.

If that fails, please follow all the self-help troubleshooting steps outlined in the Backup Now documentation page. Please do not skip any steps, they are what is actually required in 99% of trouble cases.

If that still doesn't work out, please ZIP and attach the back-end backup log file with your next post so that I can see what is going on.

Your server is not compatible with the method used to download the backup archives. I am going to add an alternate way to download backup archives is a later version. For now, you can backup but not download your archives using ARC.

Executive summary: No, it wouldn't. Actually, sending the files to Amazon S3 would prevent that error from happening.

The long version (warning! tech talk ahead!): Downloading the backup archive happens in 1Mb chunks. On a very big archive (in the several dozens of Megabytes range) ARC has to do a lot of download operations. The server sees that activity (many requests coming in per second) and thinks it is being attacked, shutting off access to the "attacker". When uploading to Amazon S3, Akeeba Backup -on your server- handles the upload. This means that on a single request, Akeeba Backup will try to take its sweet time uploading as much data as it can to S3. This makes individual backup calls to last 10-30 seconds (sometimes even more). Thus, the server "sees" a very low activity coming from ARC and won't consider it an attack, therefore it won't shut down access and you shall never see a "JSON error".