When you say, "아무 같은데", does it mean "I don't think so"?
The google translation of it was, "I think no". To a Korean speaker, would "아무 같은데" be considered the same as saying "I don't think so"?

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Answer

아무 같은데 doesn't make sense.  so your goolgling of 아무 같은데 is useless. 
but if you want to know "I don't think so" in Korean, I can suggest several things.
like these things,  아닌 거 같은데(it dosen't seem~, it doesn't look~) or 나는 그렇게 생각 안 해(I don't think so)
if you feel I am rude or not appropreate in use of Enlgish, forgive me. I can not express my thoughts completely.  have a wonderful day.