It's one thing to prefer designing only in CorelDRAW. I prefer doing most of my sign design work within CorelDRAW while using Adobe Illustrator in conjunction with Photoshop, After Effects, etc. on other projects. It's another more hazarous thing to go Corel-only, using it to open & edit customer provided art files generated by Adobe Illustrator.
CorelDRAW X7 is -slightly- better at opening .AI and .PDF files than previous versions, but it's still far from perfect. CorelDRAW X7 still trips up on complex AI gradient fills, shifting colors and stop positions along the gradient. Sometimes even the beginning and ending of the gradient can be totally out of whack. CDR X7 supports transparancy on gradient stops (finally), but even that can render oddly. Certain vector-based effects in Illustrator get rendered as pixel-based bitmaps when imported into CorelDRAW. There's no support for things like gradients on line strokes. CorelDRAW's fill percentages are in whole numbers while Illustrator can do fills in hundreths of percentage points (example C=88.75%, M=66.52%, Y=10.02%, K=13.45%). I could go on and on.
Adobe Illustrator is no better at opening .CDR files. In fact, I'd advise against it. I once hosed a Creative Cloud installation via some bug when trying to open a .CDR file directly into Adobe Illustrator CC rather than export an .AI file out of Corel. I literally had to factory reset my desktop PC from scratch to get Illustrator to launch. I haven't tried opening a .CDR file in Illustrator since then.
Artwork that is reliable to share between CorelDRAW and Illustrator: vector-art with flat fills and all text converted to curves. Generally if the artwork is more simple and not polluted with app-dependant effects it will hop between CDR and AI with no noticeable change.
A Corel-only shop can use Adobe Acrobat Reader as a fallback to proof Illustrator-generated .AI and .PDF files to see how they're really supposed to look. But that only works if the .AI file is saved with .PDF compatibility. Just drag and drop the .AI file into the Adobe Reader window.
A shop using only Adobe Illustrator has to fall back on a number of .CDR file viewer applications to proof CorelDRAW files. None of those apps are as good as having a real CorelDRAW installation.