Reaching 1000 cycles doesn't automatically trigger a free battery replacement. In fact going over it likely means they won't replace it under warranty/AppleCare because that's the nominal rating where they expect that it's going to be depleted to 80%. Typical warranty/AppleCare-provided battery replacement will be if it's under 80% battery health **and** under 1000 cycles, because that's when such depletion is expected to be atypical (i.e. "defective") if it can't achieve the nominal performance specified.
About Mac notebook batteries - Apple Support
Battery warranty information
Your Apple One Year Limited Warranty includes replacement coverage for a defective battery. If you purchased an AppleCare Protection Plan for your Mac notebook, Apple will replace the notebook battery at no charge if it retains less than 80 percent of its original capacity. If you don't have coverage, you can have the battery replaced for a fee.
Think of it like an automotive tire warranty. Those will usually specify something like "50,000 miles" and possibly discounted pro-rated replacement fees. If you hit over that 50,000 miles (akin to those 1000 cycles) the mileage warranty is no longer in force. Once you hit 1000 cycles, that means their obligation is over because depletion to 80% isn't considered it being "defective" any more.
I'd check to see what the battery health is. If it's already under 80%, then Apple will replace the battery under AppleCare, and that can be done before you receive it.