Yes, this is entirely true!
Snake growth is based on the condition known as indeterminate growth. They grow rapidly until maturity and then growth slows down but never quite stops. Plants also exhibit this same phenomenon (hence old trees getting pretty darn large).
This explains why snakes continue ecdysis (keratin skin sloughing) throughout their lives.
Interestingly, many arthropods slough their outer shell but I am unsure if they have indeterminate growth (100 year old giant scorpions anyone?)
This is one of the reasons I have a lot of respect for the giant snakes in nature because they must be very old and is very sad when people kill them.