Its usually considered polite, if you are going to respond in the negative to a question, to explain your reasoning and to add to the general conversation. In fact, this board used to have a minimum character limit to posts for just this reason.
I would love nothing more than to comment on your ideas, but it is difficult to do so when little is given. In any case, I'm going to suggest that "no" is not that correct answer. A better response would be "maybe, though its unlikely." The Germans converted to Christianity largely due to their connections to the larger, Christian, Roman culture. That, however, does not necessarily mean that they would not have done so without the Romans adopting Christianity. For instance, they might have adopted it for much the same reason the Khazars adopted the Jewish faith centuries later - to find a religion which was on an equal playing field with their neighbors, but which allowed them to stay out of a religio-cultural orbit at the same time (as well as to play two faiths against one another). I can imagine a scenario where there are two different Monotheistic faiths in the Eastern and Roman Empire, and Christianity allows the Germans to say "hey, look! We're Monotheists too. Just not like you two. Deal with it."
Also, its important to realize that, no matter how important the Roman cultural sphere was to the Germanic tribes, it was not the only important factor which drove their behavior. Perhaps Christianity takes off amongst a tribe because it meets an internal need of their people (be it cultural, political or economic). In the latter case, the religion of the Roman Empire doesn't mean a thing.
So, no, "No" is not a valid answer to this question. I still by my assertion of "Unlikely, but maybe?"