Yes, servers can respond without specifying the size by using chunked encoding. And you can do the rest with a custom web server that just handles request by returning "<div>" in a loop. I have no idea if browsers are vulnerable to such a thing.
I just tested it via a small python script sending divs at a rate of ~900mb (as measured by curl) and firefox just kills the request after 1-2 gb received (~2 seconds) with an "out of memory" error, while chrome seems to only receive around 1mb/s, uses 1 cpu core 100%, and grows infinitely in memory use. I killed it after 3 mins and consuming ca. 6GB (additionally, on top of the memory it used at startup)