I absolutely will not try to open (or import/place) a CorelDRAW .CDR file into Adobe Illustrator. Not after the hassle I went through last March.
I used to have few problems at all opening CorelDRAW .CDR files directly into Illustrator. The .CDR files would open just fine if saved to version 10 or earlier, and not have a bunch of Corel-dependent effects "live" in the .CDR file. At worst, I might have to re-build a gradient fill or two or re-fill certain Pantone spot color filled objects that opened with black fills. That's about it.
In March, after applying some security updates Microsoft released for Windows (XP thru V.8), something happened with Illustrator. I tried opening a customer provided CorelDRAW .CDR file into the 64-bit version of Illustrator CS6 and it crashed the program. Even worse, I couldn't launch Illustrator CS6 64-bit after that. Worse than that: none of my 64-bit Adobe applications would work. I ended having to perform a factory restore operation on my new Dell desktop computer and then download & install all my Creative Cloud applications all over again. Giant pain in the @$$.
One of my coworkers got hit with the same bug two months later. She tried opening a CorelDRAW .CDR file into Illustrator and it crashed all the CS6 64-bit applications. The 32-bit versions still worked. Instead of doing a factory reset we just waited a couple or so weeks for the new CC apps to become available. They worked alright. After installing them I uninstalled all the CS6 applications.
After going through that mess, I now import CorelDRAW artwork into Adobe Illustrator by opening the .CDR files into CorelDRAW and saving Illustrator CS5 format .AI files from there. I still have to re-build certain fill effects upon opening the layout in Illustrator. But it's a lot better than having the machine crash.
BTW, this problem seemed to migrate down to Windows 7 and probably other versions of Windows and Illustrator as well. I'm running Win7 Ultimate and Adobe Master Collection CS5.5 on my personal notebook computer. After that March security update Illustrator CS5.1 can't seem to open any CorelDRAW .CDR files. It just causes the program to hang. At least it doesn't hose all my 64-bit Adobe applications in the process.