The short answer to your title question is No. The rest of the try: block will not execute after an exception.
As you note, you can put code_a, code_b and code_c in their own try: blocks and handle errors separately.
You asked if code_c could run even if code_b raised an exception.
Option 1
Put code_c outside the try: block entirely:
try:
    code_a
    code_b
except:
    pass
code_c
But take care. code_c won't definitely execute. it depends what's in the except: block. Consider the following example:
try:
    code_a
    code_b
except:
    return False
code_c
return True
If code_a or code_b raise an exception, code_c will not execute.
Option 2
Use a finally: block:
try:
    code_a
    code_b
except:
    return False
finally:
    code_c
return True
If code_c is in a finally: block it is guaranteed to execute whether or not there is an exception.
If there is no exception, code_c executes after code_a and code_b.
If there is an exception, return False will work as expected BUT code_c will squeeze in and execute just before the function returns. This is because it is guaranteed to execute.
Complete Example
def ham():
    print('Ham please')
def eggs():
    print('Eggs please')
    raise NoEggsException
class NoEggsException(Exception):
    pass
def spam():
    print('Spam Spam Spam Spam Spam!')
def order():
    try:
        ham()
        eggs()
    except NoEggsException:
        print('    ...no eggs :(')
        return False
    finally:
        spam()
    return True
if __name__ == '__main__':
    order_result = order()
    print(f'Order complete: {order_result}')
When run as written, eggs() raises an exception. The result is as follows:
Ham please
Eggs please
    ...no eggs :(
Spam Spam Spam Spam Spam!
Order complete: False
Note that spam() (in the finally: block) is executed even though there is a return False in the except: block.
Here is what happens when raise NoEggsException is commented out or removed:
Ham please
Eggs please
Spam Spam Spam Spam Spam!
Order complete: True
Note that you get spam (and more spam) in your order either way.