A NAS is is a fileserver. Period.
To reduce shoe-shining, backup systems frequently back up data to a disk pool first, and then when they have enough data accumulated to fill a tape, they'll relocate that backup job to tape all in one session. The disk pool could be a NAS, or it could be a dedicated array of disks connected to a backup server.
This is not specific to logs, but to any type of data you're backing up.
Hopefully this answers your question. If it doesn't please specify exactly what you are trying to accomplish here, without letting extraneous details get in the way and confuse things.
Edit:
For web logs, two mechanisms come to mind to back them up.
- Centralized logging. You should have centralized logging in place anyway. Just configure apache to log via syslog and then you have one server which you back up all of your logs on.
- Logstash/Elasticsearch - this is becoming more of a frequent use pattern. Run logstash on your webserver, which ingests your access logs, and then ships them off to an Elasticsearch instance for long-term storage and search.