Let me put it this way:

If I were the admin of that server, and you presented your case well enough, possibly with a simple program that would monitor the logfile and send only the essential data out, I would probably be persuaded to let you run it. Or at least suggest some kind of an alternative.

If, on the other hand, I found that the server which has "a few new log entries" per minute is spending most of it's time sending it's own daily log to one user, I would make that user very, very sorry. As in bastard operator from hell sorry.

Trust me on this: talk to the people managing the server first. If you try talking to them after they've shut you down for abusing their services, you won't get anywhere.

Yes, I admin a lot of servers. No, I'm not mean. Usually.