I think there is a misunderstanding here.
Your code is fine, but it checks the cells.
The initial question  was:
"my question is, is there a way to detect  if the user  has entered/altered
values in "any" of the textboxes"

Let's say that the cells "belong" to the worksheet. So if you want to find out
a change  in the worksheet(cells), that's fine (i.e. you check the event that
belongs to the worksheet  list of events)
versus textboxes  which are controls on a userform.
In this case, you need to check other events such as David suggested (i.e.
events that belongs to the textbox  list of events).
I hope I have made it clear.