Yes, although this is not as clear as the first method.
Anything that can be done with looping can be done with recursion. So there is a recursive equivalent of a sentinel-controlled loop. Here is one way to do this:
The data values might come from a file or from user input. The recursive method would call itself for each new value. But this is not a natural fit to how reading from a file should be done. The usual iterative way is a more natural way to think of the problem, and is what you would ordinarily use.
Could a sentinel value arise as a result of computation?