Firstly, SSL has the ability to resume an earlier session, so flipping between servers will cost you a few hundred ms per request (longer if several clients are accessing the site simultaneously, since this is CPU time we're talking about).
Whether the clients will actually flip depends, though - DNS "load balancing" is fiddly business:
- if many of your users are using the same recursive nameservers, they'll get the same "first IP" hence no load balancing
- if the DNS record has a high TTL (several hours), caching nameservers will store a particular permutation of IP addresses until they expire (good so long as your users aren't all using the same recursive nameservers)
- if your users have multiple recursive nameservers configured, they may flip if each nameserver has a different "first IP" (bad)
- if you have no mechanism for removing "bad" records, and a low TTL, then if one server goes down 50% of your clients will get the "bad" server and have to wait for a timeout before they can see your site
As you can see there are various tradeoffs depending on whether you're more concerned about redundancy/failover or load balancing; DNS isn't really the best tool here - you really need the servers to share an IP using either a reverse proxy, or something like Heartbeat (assuming you're Linux-based).
An aside: if both servers are answering to the same domain then you don't need a wildcard cert, although CAs often charge more if you intend to use a cert on more than one server.