Verdict: Yes
Yes. Gmail is a website, so it works on Linux the same way it did on Windows. Chrome, Firefox and Edge are all supported and all three have Linux versions.
There was never a Gmail program to install on Windows either. You opened a browser and signed in, and that is exactly what you do on Linux. Nothing to move, nothing to convert, no mail left behind.
Google's supported browser list names Chrome, Firefox, Edge and Safari. Firefox comes preinstalled on most Linux systems, and Chrome and Edge both publish Linux downloads if you would rather stay with what you know. One small gap is worth knowing about. Google notes that desktop notifications for Gmail do not work in Safari, and offline access only works in Chrome, so if you rely on either, pick Chrome.
If you would rather have Gmail in its own window with its own icon instead of a browser tab, Chrome and Edge can both install a website as an app. That gets you very close to how a mail program feels.
If you want your mail stored on your own computer as well, Thunderbird connects to Gmail and downloads a copy you can read with the wifi off. That also gives you a backup that survives losing access to the account.
Only needed if you want mail on your own machine and offline. It connects to your existing Gmail account rather than replacing it.
Your files: Keeps a local copy of your Gmail messages. Labels appear as folders, which takes a little getting used to.
Same idea with a built in calendar, so your Google Calendar sits next to your mail.
Your files: Connects to the same Gmail and Google Calendar account. Nothing to convert.
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