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.
While a server could throttle bandwidth usage per connection, they typically do not bother. If a response is big enough that it could be effectively throttled then it's about the same impact to slower clients if a fast download just completes sooner.
Splitting a download into pieces may actually hurt your client's performance because of the way TCP operates -- it has a "slow start" mechanism that reduces throughput on new connections.
Websites that implement throttling will typically do so between their various virtual hosts (so that the download site doesn't starve out a more interactive one) or will do so based on the remote IP address.
By far the primary benefit of a download manager is that it will simply continue the download if the connection gets broken.
