If you have a look on this page there is a phone number checker (if you know the number) to see if you can get Sky Broadband.
http://packages.sky.com/surf/
If it says you can get the base package then you should be able to get it. I've not heard of people being refused as they are with Be-there for having a poor line but it's free to check.
EDIT - just re-read your OP and realised you asked if O2 reject poor lines - sorry I have no idea, assumed you meant Sky as you posted on the Sky forum??
Edited by BlankFrank (Wed 04-Jun-08 13:51:24)