I think you could do it if you wanted to because Inktober is after all a time for experimentation and everyone adapts it a bit to his need or want: it is not set in stone and nobody will hunt you down if you want to work on a recursive image ! ^^

But on the other hand, using a computer does feel a bit off and doesn't really fit with the spirit of the challenge!
Maybe you could handdraw all the recursions? That would be interesting!
Or if you have time you can do it, not count it as part of your inktober and do an other drawing that day...