If it is a standard FNMA1003, then when you sign on the bottom, you are signing that
"Certification: I/We certify that the information provided in this application is true and correct as of the date set forth opposite my/our signature (acknowledgment indicated below) on this application and acknowledge my/our understanding that any intentional or negligent misrepresentation(s) of the information contained in this application may result in civil liability and/or criminal penalties including, but not limited to, fine or imprisonment or both under the provisions of title 18, United States Code, Section 1001, et seq. and liability for monetary damages to the Lender, its agents, successors and assigns, insurers and any other person who may suffer any loss due to reliance upon any misrepresentation which I/we made on this application."
In other words under Federal Law you are committing loan fraud if you knowingly fail to disclose any debts or obligations.
When I was a loan officer one of the processors where I worked caught on that there was fraud committed on the application that another loan officer took. To make a long story short, the vice president of consumer lending ended up reporting it to the proper authorities and the husband was actually arrested! (The IRS was also contacted by the prosecutors office--under law we weren't allowed to do that--and they were in trouble for tax fraud as well before it was all said and done.

)
On the flip side I've seen where we KNEW people had not disclosed on purpose, but they claimed to have "forgotten", and depending on the DTI ratios they were either denied or had to write a letter explaining how they managed to "forget" the loan.
To me it's not worth the risk.
Anne