YES there should be a problem. Standard solderless breadboards such as those made by Global Specialties or E & L Instruments have contacts that are closely-spaced. When mounted to a metal plate, a new set of maximum voltage problems will exist. It's been a long time since I've read the spec sheet on one of these, but they are made for low-voltage applications for the most part. Your strobe may have close to 500V involved, not counting the trigger voltage which is a lot higher. You can get away with using the breadboard if it's not mounted on a metal plate and if you use terminals that are separated from the rest of the board by quite a bit. Alternatively, you can literally "float" the high voltage points off the board rather than connecting them directly to contacts on the board.
The Global Specialties or E & L Instruments boards are high-quality boards. I would expect the Asian imports to have significantly lower specifications for voltage breakdown.
Dean