Yes, the colony would most likely occupy the new oak over time (how long it would take, I'm not sure). Do keep in mind though that adding more oak on top of the chunk(s) that is already provided would probably over-oak the beer, so be cautious when doing this. If you were looking to inoculate other oak chunks you'd probably be best off doing so in a different carboy. Maybe a 5000mL flask (Y450). Make a yeast starter essentially, but just pitch the consecration oak chunk with other oak, and let it go for 2-3 months or longer? Then you could just pitch that entire thing into your next project, or just take the oak from it that should theoretically have bugs crawling all over it!
Great question leolee - thanks again everyone for your interest in the kit. We hope it turns out well for everybody!