First I have to say that the original Tamagochis had this realistic feature where if you don't take enough care of your tamagochi then it dies beacause you neglected it's needs, so "technically" the answer is: no.
BUT this version adds A LOT more! One beign the "Underworld entrence". Once there, and collected enough spookacandys to buy tickets, you can use them to go to the underworld and go to a sort of park to friend Angels and Demons. After friending them you can find in theyr friend info the option to convert your tamagochi into one of them, which makes me believe that then they wouldn't die. But I'm not sure because I never tryed.
Let me know if it worked! (*^▽^*)