Verdict: Partly
Partly. CorelDRAW Graphics Suite is sold for Windows and Mac only, with no Linux version. Corel also offers CorelDRAW Web in a browser, which subscribers can use from Linux.
Corel's own product page lists Windows 11 or Windows 10 64-bit, and recent versions of macOS. Linux is not mentioned anywhere. There was a CorelDRAW for Linux many years ago and it was abandoned, so do not go looking for it.
The same page describes CorelDRAW Web as browser-based vector illustration and graphic design, and says it is for subscribers. That means you can sign in from Firefox or Chrome on Linux and keep working with your own files, provided you are paying a subscription. It is a lighter product than the installed suite, so check that the tools you rely on are there before you make plans around it.
Your .cdr files are the problem to solve first. It is Corel's own format and support for it elsewhere is patchy. Inkscape can open some .cdr files and makes a mess of others, depending on which version of CorelDRAW saved them. The reliable move is to open each file in CorelDRAW while you still can and save it as SVG for editable artwork, or PDF if the layout must be preserved exactly. Do this file by file rather than trusting a bulk conversion.
Inkscape is the free Linux replacement for the drawing side and it is a serious program, used for logos, illustration and cutting files. Expect the tools to be arranged differently and a few Corel conveniences to be missing. Penpot is worth knowing about if your work was screen and interface design rather than print, since it runs in a browser. Krita covers the painting and bitmap side that came bundled with the suite.
The main free vector drawing program on Linux, and capable enough for logos, illustration and print artwork. Tools are arranged differently and colour management for print is weaker.
Your files: Opens some .cdr files unreliably depending on the version that made them. Export to SVG or PDF from CorelDRAW first.
Browser-based, and the better fit if your CorelDRAW work was screens and interfaces rather than print.
Your files: No .cdr support. Imports SVG.
Covers the painting and photo side that came with the suite. Not a vector drawing replacement.
Your files: No .cdr support. Handles PSD, TIFF, PNG and JPEG.
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