I would definitely continue to pay the mortgage while awaiting the loan modification. If it doesn't get approved you would then owe a few months back payments and that could be impossible to pull out of. There are a lot of options if the loan modification doesn't work.
Have you ever at any time of the life of the mortgage ever paid a larger lump sum on it or made extra payments? I have seen banks lower payments and keep the rest of the terms the same by request and at no fee.
You could also try refinancing if your loan doesn't have good terms.
Lastly, you could downsize to a smaller home. I have sellers wanting to trade homes depending on what your home is like. Obviously, I am also a Realtor so if you need someone to sell your home, I could do that too!
251-786-4673 or firstname.lastname@example.org
Yes you need to continue to pay if you have the ability. Not all modification requests are approved. It has been my experience that most are not approved and those that are result in a very minimal monthly adjustment. This just isn't a program that is working (at least in our area). So your application is certainly not going to relieve you from making that payment.