No. eM Client is sold for Windows and Mac only, with no Linux version on the download page, so you will need a different mail app on Linux.
eM Client by eM Client s.r.o. · Email & calendar · No way to run it
The eM Client download page offers Windows and Mac and nothing else. There is no Linux build to buy or try,
and the company has not published one.
The good news is that eM Client is a fairly ordinary mail and calendar program underneath, so the move is
easier than it sounds. If your mail is on Gmail, Outlook.com, iCloud or any account set up as IMAP, the
messages live on the mail server rather than on your PC. Set the same account up in a Linux mail app and
everything reappears, folders and all.
The parts that are stored only on your computer are the ones to rescue first. eM Client can export contacts
to .vcf and calendars to .ics, and both of those import into Thunderbird and Evolution. If you used POP
rather than IMAP, your old messages exist nowhere else, so export them before the Windows machine goes.
Do the export while eM Client still runs. Recovering its database later on Linux is difficult and not worth
the afternoon.
Much simpler, mail only. Fine if you mainly read and reply and kept the calendar elsewhere.
Your files: Mail only, pulled from the server. No contact or calendar import.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need eM Client. Everything else you do can move.