Every branch in PlanetScale has its own separate MySQL connection credentials first off (and conceptually just looks like a separate DB), so no. You'll be using your main production database as usual, and you'll have separate credentials for a branch where you can make schema changes like ALTER TABLE, and you "connect" to that branch with... whatever. Deploy a canary version of your app, use your SQL IDE, whatever. The main branch always prohibits changes like ALTER TABLE or CREATE DATABASE. Merging a branch where the CREATE/ALTER happened is the only way to bring changes to the production database that serves your users queries.
When you merge a branch in PlanetScale, you can still write to the database while the migration is happening, online. This is done through "Online Schema Change", but the TL;DR is that a system in the background creates the new database, reads the mysql binlogs from your original database, including all the writes, and propagates those writes to the new database with the changes applied. It does this continuously, in real time. Once the new database is caught up, the system switches over transparently to make the changes atomically appear live.[1]
The requirement is that the running application server has to be able to handle both the old and new schema at the same time. This is easy if you do something like "add a column that isn't yet used and will be soon", but harder for "dropping a column that is in use". No database alone can solve this however, you have to coordinate your application layer correctly so that it can handle the switch over when you apply the changes. But this means you can have very high uptime with e.g. blue/green deployments and staged rollouts, and you'll never have to take your DB offline for it.
It's also trite but "hundreds of writes a second" is nothing. Vitess can handle 100x that write load (probably much more) and deal with schema changes to petabyte-scale databases completely online. PlanetScale currently doesn't let you control the Vitess keyspace sharding configuration (yet) which is crucial to this but I suspect it will happen eventually. But they'll also let you run Vitess in your own K8S environment while they provide a control plane, so you wouldn't pay list price, anyway.
I do not have any affiliation with PlanetScale but it's a pretty cool product I could see myself using for my low-volume needs, just because of the pay-as-you-go model where I don't pay for e.g. RDS allocation. And I say that as a really big PostgreSQL fan.
[1] https://github.com/github/gh-ost