don't think of kai/xbc as a live alternative. think of it in the following way:
if you can get the achievements by playing system link with 2 360's side by side, than you can get it over kai/xbc. if you can't get it through system link, than you can't.
some games will have rank related achievements, and your rank can only be altered by playing ranked games over live. other games might have a rank that can be manipulated via system link. at the end of the day, its hit or miss. if you really care about the online achievements, pick up a second system and get back on live. (which you have probably already done if you have a way to sync the achievements up with the web)