PDOException: SQLSTATE[42S02] on cache_block after module install
can I use the live production system to export the cache_block table structure and then import it into my localhost?


Yes, that's exactly what you should do. Core cache tables have a common structure so you could even just duplicate cache_bootstrap or another from your local and rename it.

Don't bother importing the data as you'll want to clear caches after recreating the table anyway.

Personally I'd be tempted to also go and find out what caused it in the first place to make sure it can't happen again (and so the site can stay up to date).