The answer is yes, as long as the Recovery disks will run.

If not, find any Win7 retail installation disk, extract the ISO image using ImgBurn to create an all-versions installer to install your licensed version using the Product Key on COA sticker.

Windows 7 Universal Installation Disc - Create

The installer is mostly driver-complete, with newer arriving quickly via optional Windows Updates. Any drivers then missing in Device Manager can be found on the Gateway Support Downloads webpage for your model computer.