No, quiche is agnostic to the event framework used by the application: you have to handle socket I/O externally and hand the data you receive to the quiche connection objects which keep track of protocol state and tell you what to send back.
The sample HTTP/3 client and server included with quiche use mio, a simple crate implementing an event model similar to POSIX's poll(): https://github.com/cloudflare/quiche/blob/master/apps/src/cl...