Server (site process / DB ) can eat lot more than your (socket,TCP stack,Network adapter) unless badly designed. Better question is how menu simultaneous TCP connections can server handle.
On average linux system that critical point is 100 after degradation begins. This means it can handle more that 100 but not so efficient. It can push probably up to 180 after it begins to behave totally unacceptable.
Microsoft claims latest windows servers critical point is some ware around 500 by writing more efficient TCP stack.
But note this is a lot. If you have 150000 visitors per month that is around 5-6 simultaneous connections so if you don't have 10 times more visits you should worry about this especially if you host site on real server machine.
BUT, BUT, BUT BE AWARE!!!!!!!! sites are commonly hosted on virtual machines, and then web servers on each virtual machine can have multiple sites , so this accelerates way to critical point. Critical point I talk about stands for real machine - network adapter. In shared environment other users take their part of resources.
This is explanation why you get so poor experience when you host your site with cheep hosting provider. In order to cut expenses they tend to have as much as possible virtual machines on same real server with as much sites each can handle on other hand they have physical network adapter to push traffic for all of that.