This is not really a cut and dried question since it has various factors that can affect the answer.
For example, are you using yaws (a webserver written in Erlang)? Then it wouldn't really be an issue, except that you are tying up ports on the webserver, but threads are not an issue.
Are you using Java NewIO API, so each connection doesn't take a dedicated thread, then it won't be an issue for threads.
But, if you are tying up resources needlessly, regardless of what you are doing, then that is bad. For example, if you keep a database connection open, do some major processing, then write back, that is also bad design.
Keep resources for only as long as you need them.
If you are going to do some processing that takes a sizeable amount of time then you may want to look at a more asynchronous solution.
For example, give some unique number that the user can use to check if their request is done, so they can shut down their computer, or just check it whenever they want, without worrying about losing anything.