It does help conserve battery but so long as the app is closed and not running in the background it won't consume much battery power, it does use RAM but Android manages itself very well when it comes to RAM.
The stock Play Music app actually has a couple of ways that it can be closed as it has no in app exit button of it's own, you can just pause the music and press the back button but actually this leaves a process running, processes should on the whole be left alone but there is a way to stop this process without a task killer and without any ill effects.
First once you've closed the music app with the back button tap the two squares in the nav bar to open the recently used application list and swipe the Play Music app tile to the left or right, this will fully close the app including the process.
The second way is to minimize the music app with the home button and you'll see a Play Music notification in the statusbar, pull the statusbar down to open notifications and you'll see an X on the top right side of the apps notification tile, press the X to fully close the app even with the audio playing.
I would suggest playing around to find ways to close apps without the use of a task killer, open the Apps option in settings to see what is running.
Menu> Settings> Apps> Running...
On the whole though Android does manage itself very well.
EDIT: Okay I'm going to backtrack on that second method, I've just tested it and in actual fact it leaves processes and services running so use the first method or if you do close using the X in the notifications to completely close the Play Music app swipe the tile as per option one.