The biggest threads on therpgsite have managed in the 700s in replies.
They're bullshitting, though - the number of replies to a thread has no particular effect. 10 threads of 100 posts actually take up slightly more space than 1 thread of 1,000 posts, just as if you create 10 different text files with the same text on your computer, it takes up more space than the same text 10 times in one file. That doesn't have much effect, though, it's only a fraction of a percent difference in the data size.
What slows things down is when it has to look lots of things up. Remote-linking heaps of images does that. A search function also does that, which is why they removed it at rpg.net. If you're just looking at one thread, however long it is, it's not very demanding on the software.
The number of threads and posts they have overall clutters things, because it's all stored on their server. This is why lots of forums cull old threads. But if you keep everything, well... it's just like if you keep every newspaper you ever read, pretty soon it's going to take you a long time just to find today's paper.