If your public network is enabled to also carry
heartbeats, then it should be a non-issue. You can check
this in Cluster Administrator by right-clicking the
cluster name and go to properties. Then under the Network
Priority tab, it should have both your public and private
networks listed (Private should be first). Highlight the
Public network and click properties. It should be set to
Enable All Communications.

When you first boot up before the card is configured, the
cluster won't recognize it as the private nic. However,
once it is configured, it should just connect right up.
Just make sure you configure the new card with the old IP
address/subnet mask and there won't be any difference to
the cluster.

Once the first card is done and communicating, you should
be able to failback and replace the second card and away
you go.