The boot-time scan is quite thorough, so you should be OK as presumably you have also run avast & MBAM scans in normal mode.
The win32:funweb is adware and that is what was likely to have been initiating the connection with that IP (Oversee.net), though that can't be confirmed.
The avast network shield has its own list of malicious sites, but that won't go into the same depth as MBAM's IP block as that also look at adware/reputation, where avast is specifically about blocking known malicious sites.