Our infrastructure is designed to handle dozens to thousands of indexing operations per second. The speed depends on a lot of factors, and it generally take more time using a mutualized plan than an Enterprise plan (the processing threads are shared in a mutualized plan).
In most cases, indexing operations are processed in a matter of seconds (search operations are processed in a few milliseconds). Also, while the search queries are synchronous, the indexing operations are asynchronous. You can use the method waitTask of our API clients to check when an indexing operation is completed.