Is it possible to add a subdomain to Route53 using the AWS PHP SDK?

Yes, this is possible using the changeResourceRecordSets call, as you already indicated. But it is a bit clumsy since you have to structure it like a batch even if you're changing/creating only one record, and even creations are changes. Here is a full example, without a credentials method:

<?php

// Include the SDK using the Composer autoloader
require 'vendor/autoload.php';

use Aws\Route53\Route53Client;
use Aws\Common\Credentials\Credentials;

$client = Route53Client::factory(array(
    'credentials' => $credentials
));

$result = $client->changeResourceRecordSets(array(
    // HostedZoneId is required
    'HostedZoneId' => 'Z2ABCD1234EFGH',
    // ChangeBatch is required
    'ChangeBatch' => array(
        'Comment' => 'string',
        // Changes is required
        'Changes' => array(
            array(
                // Action is required
                'Action' => 'CREATE',
                // ResourceRecordSet is required
                'ResourceRecordSet' => array(
                    // Name is required
                    'Name' => 'myserver.mydomain.com.',
                    // Type is required
                    'Type' => 'A',
                    'TTL' => 600,
                    'ResourceRecords' => array(
                        array(
                            // Value is required
                            'Value' => '12.34.56.78',
                        ),
                    ),
                ),
            ),
        ),
    ),
));

The documentation of this method can be found here. You'll want to take very careful note of the required fields as well as the possible values for others. For instance, the name field must be a FQDN ending with a dot (.).

Also worth noting: You get no response back from the API after this call by default, i.e. there is no confirmation or transaction id. (Though it definitely gives errors back if something is wrong.) So that means that if you want your code to be bulletproof, you should write a Guzzle response handler AND you may want to wait a few seconds and then run a check that the new/changed record indeed exists.

Hope this helps!