>or it would have to be upgraded to be able to read digital signals?
By adding a Freeview box you have upgraded it to receive digital signals.
Your TV is analogue, and the "old" channels you received were also analogue.
The "old" analogue signals will be switched off over the next couple of years to be replaced by digital signals.
But your freeview box can receive digital signals and play them through your existing TV so you are OK.
If anyone tells you that you need a new TV then just ignore them, particularly if they work in a shop selling TVs !