I've spent the better part of an hour looking for a definitive answer to this question. A script I need to use requires the IonCube loader be enabled and I've grown quite fond of APC.
Should I expect any problems if both are enabled on the same server?
No, if your files are encoded with ionCube you won't be able to use APC.
Besides, it is useless. Why would you want to use ionCube (unless you are using software encoded with it)?