Hi,
I’m not sure what the technical limitations are for the conditional fields plugin so you may want to check on that plugin’s support forum. The free version of this plugin has a limit of passing about 4 kb of data. Once you get the form working you would have to get the pro version which has a limit of 5 mb of data.
That being said you would have to do a lot of manual coding with the Contact form 7 plugin. I would suggest trying to find a plugin that better supports what your doing. Formidable Forms Pro is one such plugin, there’s also Gravity Forms and others that handle multi step forms and conditional logic in its core.