That will most likely depend on the device, a generic answer valid for all of them cannot be given. For example, the Samsung Galaxy S2 specs give 32 GB as max, still some user was able to get a 64 GB card working (see: 64gb SDXC Cards in Galaxy S264gb SDXC Cards in Galaxy S2). For some older devices, the 32 GB limit might be a fact, while again others might just have specified it to be "on the safe site".
TL;DR: Yes, it's device dependant, some devices have their limits.