How likely is it that there will be an problem?
If the system is idle, most likely it won't be a problem. An unclean power-off is like rolling dice -- snake eyes and you lose. But most of the time you won't. So if you are asking, "Is there a way I can guarantee this is okay?", the answer is no (but see the final paragraph, below). If you are asking "Is this worth the risk?" when it sounds like you don't have a choice, the answer is if you don't have a choice then it is a risk you will have to take.
In ideal terms, I do not believe the pi is any more prone to corrupting a filesystem when the power is cut than a normal computer, and the same factors apply: If the system is very busy at the time, the chance of corruption is greater. I say "in ideal terms" because I think if some of the power problems associated with the pi contribute to corruption, then the story may get a little different. The solution to that presuming there's not also some quality control issue, is to use a proper power supply.
I have not done a formal survey, but I think reports of problematic corruption have diminished a bit this year. There's then this issue to consider, which I have not investigated further. It's no longer an issue and may never have been (but it may also have been very significant).
Note that the kernel bug issue doesn't depend on cutting the power and the insufficient power/possibly defective hardware issue probably doesn't either, meaning that might have been coincidentally blamed in a lot of the cases online.
You might be interested in this recent answer from someone who claims to be involved with some decent scale commercial application where they cut the power all the time and have not had any problems. This hints at the fact that people who don't have a problem will not post a Q&A online, "Everything worked fine again today: Why?".
If feasible, using read-only filesystems should (again: in "ideal terms"1) eliminate the risk. But this may be another thing about which you don't have a choice.
1. We've had at least a few people here report corruption when killing the power even with a read-only filesystem, which should not happen. This implies a hardware or software defect, as outlined above, is responsible in some cases, which will probably never affect most people.