Does transferring files over a local network use up internet bandwidth

We've got a server on our network and some drives on that server mapped to our desktops. When I transfer a file over, windows task manager reports 100% network utilization on local area network, which is great.

How can I check whether this consumes internet bandwidth or not?

You can disconnect your Internet, and should find that it still works fine, unless there is some strange reason the server relies on the Internet.

Depending on your router, it could slow down the network, including Internet access, for other users, but will not affect the Internet connection.

Short answer is no it should not.

Local network usage does not constitute internet usage, so just disconnect your cable / adsl line and test. It should still be pumping the data at full capacity, but it should not be using the net for it.