In any case binary (1/0) variables can be analysed as such in any multivariate approach see: Cox, David R. "The analysis of multivariate binary data." Applied statistics (1972): 113-120.
Yes, it is possible to perform canonical correlation analysis (CCA) with two sets of binary variables. According to a post on Stack Exchange, it is okay to use standard CCA with data that are partly or all binary variables. Since a binary variable has only two levels, it behaves identically whether it is seen as numeric or categorical.