Will Box Drive or Box Edit cache files on the local machine?
Box Drive does locally cache files that you have opened. Box Drive's cache size limit is based on your free disk space (50% of available space) and has a maximum limit of 25 GB. If you reach this limit, Box Drive begins removing files, starting with those files files that have gone the longest without your accessing them. Also, if a cached file has a new version created on Box, Box Drive discards the locally cached version. Do not open data in Box Drive containing restricted data. More details: Technical Information for Box Drive Administrators
Box Edit does download the file to a cache when you are modifying a file. The cache can be cleared. See: Clear Your Box Edit Cache