It depends on how you define "cause". Can it have some observable effect? yes.
As Hans and Sneftel pointed out - exceptions, interrupts, traps, etc.. are all taking place at retirement, to which a wrong-path code would never reach. So a mispredicted branch can't cause a commit / retirement of wrong path instruction, including any illegal opcodes they may attempt to execute.
However, it is possible for a mispredicted code path to affect the micro architectural state in more subtle ways, you may have loads performed and cached, page walks done, and various other micro architectural events - in short, all the hard work your CPU does while you carelessly go and mispredict some branch (which is quite a lot in OOO CPUs). I highly doubt that any CPU out there is going to go and fish all this stuff out of your caches/TLBs, so take into account that these things can later have an effect on the performance of your program (for good or for worse), just not on its functional behavior.
It's probably not worthwhile if you're in the business of optimizing performance (and probably too complicated to make any use of), but it may be relevant to consider if you're in the business of securing your code - some hackers may have ways to sniff such data from your caches.