I don't think 600 people is small enough for you to encounter the genuinely terrible ways that actual small companies are run, so you should be OK. I'd be focusing on the number of staff at the location you are going to be based at, the attitudes to training and the budgets to go along with that etc.
A decent role in a 600-person org. sounds ideal, it's likely big enough to have the sort of talent pool that you need to be successful in your own role, not so big that you end up with faceless entities making decisions that affect you, and not small enough that you end up carrying tons of people or are the only person doing your job. I'm obviously making a lot of assumptions but I assume you haven't had any alarm bells going off at the interview stages?