The idea behind breaking up a download into multiple segments with different ranges is for increasing download speed. This works if the server has a per connection limit. A server without that limitation theoretically servers the same bytes with one or more connections.
My question is if download managers still speed up downloading from such a server or it's just a useless effort. In other words is there any limitations per TCP socket connection by default or not?
No. There are no limitations per socket. Most OS:es will try to share the bandwidth equally between all sockets unless QoS is specified.