是的，Apache Commons HttpAsyncClient支持GZIP压缩。以下是一个示例代码，演示如何使用HttpAsyncClient进行GZIP压缩和解压缩：

import java.io.ByteArrayInputStream;
import java.io.ByteArrayOutputStream;
import java.io.IOException;
import java.nio.charset.StandardCharsets;
import java.util.zip.GZIPInputStream;
import java.util.zip.GZIPOutputStream;

import org.apache.commons.io.IOUtils;
import org.apache.http.HttpEntity;
import org.apache.http.HttpResponse;
import org.apache.http.client.methods.HttpPost;
import org.apache.http.concurrent.FutureCallback;
import org.apache.http.entity.ByteArrayEntity;
import org.apache.http.impl.nio.client.CloseableHttpAsyncClient;
import org.apache.http.impl.nio.client.HttpAsyncClients;

public class GzipCompressionExample {

    public static void main(String[] args) throws Exception {
        // 创建HttpAsyncClient
        try (CloseableHttpAsyncClient httpclient = HttpAsyncClients.createDefault()) {
            httpclient.start();
            
            // 创建要发送的数据
            String data = "Hello, world!";
            byte[] compressedData = compressGzip(data);
            
            // 创建HttpPost请求对象
            HttpPost httppost = new HttpPost("http://example.com/api");
            httppost.setHeader("Content-Encoding", "gzip");
            
            // 设置请求体为压缩后的数据
            httppost.setEntity(new ByteArrayEntity(compressedData));
            
            // 发送请求
            httpclient.execute(httppost, new FutureCallback() {
                @Override
                public void completed(HttpResponse result) {
                    try {
                        // 获取响应体
                        HttpEntity entity = result.getEntity();
                        byte[] responseData = IOUtils.toByteArray(entity.getContent());
                        
                        // 解压缩响应数据
                        String response = decompressGzip(responseData);
                        System.out.println("Response: " + response);
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                }
                
                @Override
                public void failed(Exception ex) {
                    ex.printStackTrace();
                }
                
                @Override
                public void cancelled() {
                    System.out.println("Request cancelled");
                }
            });
            
            // 等待请求完成
            Thread.sleep(5000);
        }
    }
    
    private static byte[] compressGzip(String data) throws IOException {
        ByteArrayOutputStream baos = new ByteArrayOutputStream();
        try (GZIPOutputStream gos = new GZIPOutputStream(baos)) {
            gos.write(data.getBytes(StandardCharsets.UTF_8));
        }
        return baos.toByteArray();
    }
    
    private static String decompressGzip(byte[] data) throws IOException {
        ByteArrayInputStream bais = new ByteArrayInputStream(data);
        try (GZIPInputStream gis = new GZIPInputStream(bais)) {
            return IOUtils.toString(gis, StandardCharsets.UTF_8);
        }
    }
}

在上述示例中，首先使用compressGzip方法将要发送的数据进行压缩，然后在HttpPost请求的头部设置Content-Encoding为"gzip"，并将压缩后的数据设置为请求体。然后使用HttpAsyncClient发送请求，并在回调函数中获取响应数据。最后，使用decompressGzip方法对响应数据进行解压缩。