Definitely, yes. The thing is web pages tend to refresh every once in a while, and so they use a small percentage of your data. It is strongly advised to close any app or browser when you are not using your mobile device.
To add a bit on what @Anonyme started. (about closing apps when you leave them)
If you possess an android device, you could always active the developper options in the settings (see bellow) and then scroll through the dev options to activate the "don't keep activities - force quit every activity on exiting apps"
It does pretty much what it says
-----How to activate dev options-----
Go to the settings menu, and scroll down to "About phone." Tap it.
Scroll down to the bottom again, where you see "Build number."