Verdict: Yes
Yes. Google Docs has always run in a browser, so it works on Linux exactly as it did on Windows. There is no desktop program to install on any operating system.
Google Docs, Sheets and Slides have no installed version for Windows either, so there is nothing to replace. Open Firefox or Chrome on Linux, sign into your Google account, and your files, sharing and comments are all there.
Offline editing is the one thing to set up. Google's offline mode needs Chrome or Microsoft Edge with the Google Docs Offline extension, and you turn it on from Drive's settings while you are still connected. Firefox cannot do offline editing, so if you work on a train or somewhere without a connection, install Chrome on Linux and use that for Docs.
Nothing needs moving across, because your documents live in Google Drive rather than on the PC. If you also had the Drive for desktop program syncing files to a folder on Windows, that program is Windows and Mac only, and Insync or rclone are the usual Linux answers for keeping a synced folder.
For work that has to stay on your own machine, LibreOffice and ONLYOFFICE both open and save Google's exports of .docx, .xlsx and .pptx files.
Free and installed on your own computer, with no account and no connection needed. No live shared editing with other people.
Your files: Opens the .docx, .xlsx and .pptx files Google Docs exports, and saves back to them.
Closer to a modern ribbon layout, and it can connect to a Nextcloud server for shared editing if you want that.
Your files: Built around the Office formats, so Google exports round-trip with little change.
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