Ok, since you are so desperate for an immediate answer, I will give you my best GUESS. That is all this is, a guess. I take no responsibility for what I am about to say...
I vote NO, because you cannot be sure if there is anything else living in that filter, or if the turtle is a carrier of a disease/parasite/etc... (carrier means they are not affected by it) of something that can affect fish. Also, there may be other "stuff" in the filter besides the bacteria you want. I know turtles skin often looks dry and kinda flakey, so possibly dead skin (like I said, totally going out on a limb here).
With fish, I think it is always best to be cautious and patient. It is better to have something take longer than to get it done quickly but have problems down the road.
If you are trying to save the bacteria until you get a better answer, you can put the bio bag in a bucket with a little PURE ammonia. In cycling my tank, I needed ~ 3 teaspoons for a 20 gal tank to get a concentration of 5 ppm.