Yep that's fine - there's 2 parts to Windows the physical disk and the license key.
The license key is the important bit. So you can install as many times as you like, from different Windows 7 media if you like on the laptop, just remember to use the same license key on the same machine.
It's not even needed straight away, you can skip it during the install, and it will work for 30 days no problems, which can be extended. Eventually though you'll need the key and it will activate your copy of Windows with MS.
On your Acer machine you should find a sticker on the bottom of the machine with your key listed. You might want to just double check with a keyfinder that it's the one that's registered in Windows at the moment.
Just don't waste two keys on one machine