They can't find out what debt he has. When a company does a credit check on you, the credit report will show everytime a company has performed one. This includes anytime you have applied for a:
Mobile phone contract
Interest free arrangement
It can also show ongoing credit agreements you have with companies.
Eg: I have a Citibank Credit card and they update my credit file each year to say they have an ongoing credit arrangement with me. But not all companies do that.
The bank will not do anything if they find out he has more debt than he stated, however, if he signs a contract stating that he was trueful in what he told the bank, and then it ever comes up that he wasn't, the contract could be considered null & void, and that could become bad if there is ever any payment problems with the mortgage etc.
Its never a good idea to lie about that kind of thing, especially taking on more debt.
Trust me I know from personal experience, it can become a spiralling problem.