If you are indeed on a dedicated box with reasonable hardware then I would imagine that 30k users over some minutes is perfectly ok with a properly configured server - obviously this is a very general statement, a lot depends on the specifics of you site obviously, and your users will, I'm sure, notice some slow down but I wouldn't have thought the server will give up the ghost all together. They key is in configuring it properly. Here is a snippet from my server's httpd.conf:
StartServers 32
MinSpareServers 10
MaxSpareServers 30
ServerLimit 1024
MaxClients 1024
Now, this is a very powerful machine, but it will easily handle hundreds of requests per second. The key is the MaxClients (and ServerLimit since MaxClients cannot be > ServerLimit), however you can't just go raising this arbitrarily since if you use up all of the server's RAM Apache will start using the hard disk as mentioned above and that == sloooooow. You need to figure out how much RAM an apache process is using and make sure you have enough RAM to cover the MaxClients setting. You can do this via a shell with the following command (obviously change the httpd in the first grep if your server process is named differently):
ps -ef | grep httpd | grep -v ^root | awk '{ print $2 '} | xargs pmap -d | grep ^mapped: | awk '{ print $4 }' | cut -dK -f1 | awk '{ SUM += $1} END { print SUM/NR"KB" }'
You can then divide your available RAM by this figure for a rough guide. Bear in mind though this is available RAM, ie after accounting for the other running processes, notably MySQL which is the biggest RAM hog on my server (so it may be worth making sure all your tables are nicely indexed too to save on resources consumed there).
If you Google for "apache performance tuning" and similar I'm sure you will find lots of other resources too.
IMO it will be far preferable if you can keep your server up. If it is overloaded, people are not going to get anything except error messages from their browser.
BTW in case you are not aware of it, ApacheBench is a very useful tool for testing your configuration. You might also want to whip up a PHP script to hammer your server with HTTP requests and see how it copes with the load (just discard the response data).
If tuning doesnt look like it will get you what you need, then I'd agree with the above and look into load balancing, but that is not without its own issues. Generally though you can get a lot from the LAMP stack by configuring it properly and not sticking with the default settings.