Can Postgres index regular expressions stored in a column?
Short version: no. There's no practical way (in PostgreSQL, at least) to index a pattern column so it can be matched against plaintext inputs in a way that will speed up "does this plaintext match any of these patterns" queries.

PostgreSQL would need a special custom index type that "understood" pattern matches. I'm not sure how practical it'd be to implement one, nor how much could be gained from such an index. Since there isn't one, the question is somewhat academic.