Can you tell me what is the impact of a mismatch between the analyzer configuration in Elasticsearch and the one in Hibernate Search?

If you disable schema management, there shouldn't be any impact whatsoever. Analyzer handling on the Hibernate Search when using Elasticsearch is purely declarative, we manage names and know little of what's behind.
Disabling schema validation may hurt in the long run, though, since you won't be warned about other mismatches in your schema. But you already know this.

On a related note, I noticed that using a Discriminator for index-time analyzer selection not only does not work with Elasticseatch but also seems to make some of the fields included in the class bridge be excluded from the request to ES (even though the underlying Document has the fields).

This is weird, especially because search doesn't not involve analyzer discriminators at any point. Could you please create a JIRA ticket, ideally with a failing test case? We have test case templates available at https://github.com/hibernate/hibernate-test-case-templates/tree/master/search. Thanks!