It might damage it. That oil doesn't look good and like Dragon wrote above, it looks like engine oil.
If I were you, I'd pull the trans pan plug and drain it into a clean container with the thought of possibly reusing what you drained. Then I'd drop the pan and take a look at the 2 magnets attached to the bottom of the pan.
If the bottom of the pan is decent and the 2 magnets have very little material on them, I'd;
put it all back together, add back all the trans fluid you pulled out, pull the plug again, drain the 3-4 quarts that will come out from just a plug pull and then refill it with new fluid.
If the bottom of the pan looks like

and the magnets look like

, then the trans may very well be

and it's a roll of the dice as to whether or not the trans can take new fluid. At least you've got all the old stuff to add back in.
If you recently bought this FX, I'd verify whether that trans oil is in fact trans oil 1st cause that shit looks like fuck'n engine oil. Smell it. Taste it. Pour some on the floor and roll around in it. Become one with the oil. Let it speak to you. Make love to it. Get all up in that oil and make t your bitch.

Only then will it reveal it's true nature, only then will you know if this is in fact trans oil and not engine oil that some ignorant jackass put in your transmission.
