Can I recover CDC tables from transaction logs?
Transaction logs are used as a source to get the data CDC uses but it would be very difficult to extract data yourself and insert it into CDC tables. 

Problem is that transaction log is not well documented and there are basically two functions you can try DBCC LOG and fn_dblog.
Another option is to use a third party log reader such as ApexSQL Log or Quest Toad but even with those tools you’ll be only able to read what’s written in transaction log. It would be up to you to take this data and somehow add it to CDC tables.