Is it possible to bulk update a table using WP Rest API?

Having a huge amount of data is a problem only if you need to give back a meaningful response. If you do not have to, you can just save the request and process it with some kind of a cron job.

Is 1000 rows (whatever that means) is a lot of data? that actually depends on what is it that you need to do with it and the abilities of your server. By itself no amount of textual data should be “huge” for modern servers and software (unless you are talking about google and the like).