Do I get access to the raw data?

Multi Channel Conversion Attribution does not track any new data and does not add any new log tables to your Matomo (Piwik). The reporting is entirely generated based on your existing data.

Therefore, the raw data is accessible as usual by using the Matomo Live Reporting API. Additionally if you host Matomo yourself, you get access to all data that is stored in your MySQL database: the data is stored in the matomo_log_* tables.