Can I use OpenSSLs SSL library with non-blocking I/O?
Yes; make sure to read the SSL_get_error(3) manual page! A pitfall to avoid: Don’t assume that SSL_read() will just read from the underlying transport or that SSL_write() will just write to it — it is also possible that SSL_write() cannot do any useful work until there is data to read, or that SSL_read() cannot do anything until it is possible to send data. One reason for this is that the peer may request a new TLS/SSL handshake at any time during the protocol, requiring a bi-directional message exchange; both SSL_read() and SSL_write() will try to continue any pending handshake.
