No,
If there is no cardinality defined that mean, BO tool i.e. Universe Design Tool, by itself will not be able to detect whether there could be possible trap or not.
traps depends on data and relationship between two tables.
Cardinalities in universe structure is just a representation of the relationship.
For eg. Lets say a trap is there A--<B--<C in a,b and c table.
When you set cardinality in universe, and with this structure , when you do integrity check, a possible divergence(trap) message will be given by universe.
If you dont set the cardinality , trap will still be there only that Universe toll will not be able to detect it during integrity check.
Results in both cases will be same that is TRAP.
I hope it is more clear now.
Thanks
Gaurav