When using an HSM with TLS all cryptographic operations involving the private key are executed on the HSM. This means the private key never leaves the HSM. In fact, the HSM is specifically designed to protect exfiltration of the private key using software based attacks and sometimes even hardware based attacks (i.e. tamper resistant). This exactly is the reason a HSM is used at all.
This means that an HSM would not be worth its money if it would be possible to extract the private key using OpenSSL or other tools or even by using specifically designed hacking tools. Thus the answer to your question for all existing HSM is hopefully: No, it is not possible to extract the private key using software.
Which means: if you need both more performance and the security of an HSM for every TLS connection then get a faster HSM.
