Actually no: you can look all you like without paying, it's just kind of clumsy. If you "export your data from Slack" (yourteam.slack.com/services/export), you get the whole history, even on the free plan.
I've repeatedly considered writing a bot that would—on a regular schedule—poke this page with a headless browser to generate a dump, download said dump, and ingest it into ElasticSearch (which I'd then expose through a web search, or maybe just spit out batched archive pages into a static-site S3 bucket and let Google index them.) Such a bot would be a good companion to https://github.com/rauchg/slackin for FOSS teams.
But I haven't done any of that yet, because I get the feeling that putting enough attention on this little "feature" would get it quickly locked down.