Right now, no - we limited this non-Alternator-tables interface only to internal system tables, and only to reads, and do not allow it for non-system tables.
Part of the problem is security (what if the CQL tables have access control rules?), but a more mundane problem is that we did not yet want to commit on how this ad-hoc interface was supposed to work. The different front-ends (CQL, Redis, Alternator) not only have different tables, they also have different types, different data models, and if we allow some sort of translation between the three, we will need to officially document how it works - and also commit to stability of this API.
If you do have a use case that would benefit from access (read-only? also write?) to Redis (also CQL?) tables from Alternator, please open an issue requesting such a feature with as many details as you can to make a convincing case that this is a useful feature.