If you have a few HA proxy nodes with DNS load balancing, wouldn't the client auto move on to another HA proxy? It is a tiny lag but shouldn't be an error.
That might have been the case if you could expect clients to be well behaved, but you can't. In my experience, hardly no network clients handle that kind of thing properly.
No, once the client has resolved the IP it will either connect to that proxy or fail that particular connection attempt. But you can use the DNS to drain a proxy before restarting it.