Verdict: Partly
Partly. There is no Grammarly app for Linux, but the browser extension and the web editor work in Firefox or Chrome on Linux, which covers most of what people use it for.
Grammarly's desktop app is Windows and Mac only. Its own download page offers those two and nothing else. So the thing that watches every program you type in does not come across.
The browser extension does. Grammarly publishes it for Chrome, Firefox, Edge and Safari, and the first three all run on Linux, so your writing gets checked in webmail, in social media, in web forms and in Google Docs the way it does now. The Grammarly editor on the web works in any of those browsers too. If you pay for Grammarly Premium the subscription covers the extension and the web editor as well as the desktop app, so you are not paying for something you have lost access to.
The gap is offline writing. Anything you type in LibreOffice or a desktop mail program is outside the extension's reach, and there is no Linux app to close that.
LanguageTool is the usual answer for that gap. It has browser add-ons for the same browsers, and it also plugs into LibreOffice and Thunderbird, which is exactly where Grammarly cannot go. Its free tier covers spelling and basic punctuation and style, with deeper checking behind its own Premium. The checking engine is open source and can be run on your own machine if you would rather your writing stayed there, though that takes some setting up.
Same job, and it reaches LibreOffice and Thunderbird as well as the browser, which Grammarly on Linux cannot. Free tier is thinner than Grammarly Free feels.
Your files: Grammarly's saved documents live in your Grammarly account and stay reachable through the web editor in a Linux browser.
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