Verdict: Yes
Yes. Google Sheets is a website, so it works on Linux exactly as it did on Windows. Google supports Chrome, Firefox and Edge, and all three run on Linux.
Sheets was never a Windows program. It runs inside the browser, which means the machine underneath it makes no difference. Sign in with the same Google account on Linux and your spreadsheets are there.
Google lists Chrome, Firefox, Edge and Safari as supported browsers. Firefox comes preinstalled on most Linux systems and Chrome and Edge both have Linux downloads, so you have a choice. Google notes that Firefox and Safari miss out on offline access, so if you work on spreadsheets on a train or a plane, use Chrome and turn offline mode on before you leave.
One small thing worth knowing. If you had installed Sheets as a desktop shortcut on Windows, you can do the same on Linux. Chrome and Edge both offer to install a website as an app, which gives you a plain window and an icon in your menu rather than another browser tab.
If you would rather not depend on a connection at all, LibreOffice Calc and ONLYOFFICE both import files downloaded from Sheets in .xlsx form.
Only worth it if you want your spreadsheets stored on your own machine rather than in a Google account. No live sharing.
Your files: Opens .xlsx and .csv files exported from Sheets. Formulas usually convert, scripts do not.
Has its own online version with shared editing if the collaboration was the point of using Sheets.
Your files: Opens .xlsx and .csv exports from Sheets.
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