Can python throw a “stack overflow” error?

You can, if your recursion limit is too high:

def foo():
    return foo()


>>> foo()

Result:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  .......
  File "<stdin>", line 2, in foo
RuntimeError: maximum recursion depth exceeded
>>> 

The default recursion limit is 10**3 (verifiable via sys.getrecursionlimit), but you can change it using sys.setrecursionlimit:

import sys
sys.setrecursionlimit(10**8)

def foo():
    foo()

but doing so could be dangerous: the standard limit is a little conservative, but Python stackframes can be quite big.