<p>From what I understand, if you have multiple web servers, then you need some kind of load balancer that will split the traffic amongst your web servers.</p>

<p>Does this mean that the load balancer is the main connecting point on the network? ie. the load balancer has the IP address of the domain name?</p>

<p>If this is the case, it makes it really easy to add new hardware since you don't have to wait for any dns propogation right?</p>

There are several solutions to this "problem".
You could round-robin at the DNS-level. I.e. have www.yourdomain.com point to several IP-addresses (well all your servers).
This doesn't give you any intelligence in the load balancing, but the load will be more or less randomly distributed, but you wouldn't be resilient to hardware failures as they would still require changes to DNS.
On the other hand you could use a proxy or a loadbalancing proxy that has a single IP but then distributes the traffic to several back-end boxes. This gives you a single point of failure (the proxy, you could of course have several proxies to defeat that problem) and would also give you the added bonus of being able to use some metric to divide the load more evenly and intelligently than with just round-robin dns.
This setup can also handle hardware failure in the back-end pretty seamlessly. The end user never sees the back-end, just the front-end.
There are other issues to think about as well, if your page uses sessions or other smart logic, you can run into synchronisation problems when your user (potentially) hits different servers on every access.