Write a Python function `count_odd_binary_rotations(binary_string, rotations)` that takes a binary string and a number of rotations as input. The function should determine how many of the rotated versions of the binary string represent an odd number when interpreted as a binary number.
A binary string is considered odd if its last character is '1'. Rotating a binary string means moving its last character to the front.
#### Example Usage
```python [main.nopy]
count_odd_binary_rotations("1011", 4) # Output: 3
count_odd_binary_rotations("1100", 4) # Output: 2
count_odd_binary_rotations("0000", 4) # Output: 0
```
#### Constraints
- The input binary string will only contain '0' and '1'.
- The number of rotations will be a positive integer equal to the length of the binary string.