Verdict: No
No. Adobe lists Illustrator for desktop and iPad only, there is no Linux version, and it does not run reliably through Wine. Inkscape is the free replacement most people end up using.
Adobe's Illustrator page mentions the desktop app and the iPad app and says nothing about Linux. There is no installer, no subscription tier that unlocks one, and Adobe has never signalled any interest in making one. Running it through Wine, the tool that coaxes some Windows programs into working on Linux, is not a route anyone should rely on for paid work.
Inkscape is the answer for drawing with shapes and curves, which is what Illustrator is for. It is free, installs from your Linux app store in one click, and covers logos, icons, diagrams, cutting files and print artwork. It is a real tool used professionally. It is also visibly less polished than Illustrator, its text handling is fussier, and preparing files for commercial print in the CMYK colour system takes extra steps.
The easiest path for a non-technical user is to install Inkscape, open your old files in it, and give yourself an afternoon with a tutorial. Nothing you learn is wasted, since the underlying ideas of paths, nodes and layers are the same.
Your existing .ai files usually open. Illustrator has for years saved a PDF copy inside the .ai file, and Inkscape reads that. Shapes, paths and colours come through. Editable text sometimes arrives as outlines, and Illustrator-specific effects and brushes do not survive. Before you leave Windows, save your important artwork as SVG or PDF as well, which travels much more cleanly.
Free, open source and the standard Linux drawing tool. Same job, different habits, and a genuine adjustment period.
Your files: Opens most .ai files by way of the PDF data inside them. Text may come in as outlines and special effects are lost. SVG and PDF exports transfer much better.
For painted and illustrated artwork rather than shapes and logos. Not a drop-in for technical drawing.
Your files: Does not open .ai files usefully. Works from images and its own format.
Only if your Illustrator work was really image editing. It works in pixels, not curves, so logos will not scale the same way.
Your files: Can import PDF exports as flat images. No editable vector support.
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 Adobe Illustrator. Everything else you do can move.
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