Yes, but it may not provide the sort of load balancing you have in mind. The answer if two different Tors have the same hidden service private key is that they will each publish a hidden service descriptor.
How does a Tor hidden service work?
Tor hidden service allow users to publish their service without revealing their identity (IP address). Users can connect to this service using rendezvous point without knowing the publisher of service and revealing their identities.
What is a hidden service?
Servers configured to receive inbound connections only through Tor are called hidden services. Rather than utilizing a server's IP address (and thus its network location,) a hidden service is accessed through its . onion address.
What is hidden service protocol?
Hidden Service Protocol. The hidden service creates a Service Descriptor containing it's Public key for Authentication and the IP Addresses of the Relays acting as introduction points. The Service Descriptor gets signed with the hosts private key.