See this my question (and answer): How browsers handle multiple IPs.
Shortly - round robin dns does not improve availability at all. Browser chooses one IP and sticks to it, even if it does not responds. (Checked with FF and chrome).
Once browser dns cache expires, hostname resolved again and the process repeated, regardless of did IP answered or not.
For basic HA, you may use dynamic DNS or various IP-based approaches.
EDIT: This behavior will take place when inaccessible host acts as a "black hole". If instead the host ctively refuses incoming connections, browser will try one ip, get refuse and immediately use another ip and thus it will fail-over pretty well.