Not at all. If anything, the opposite would be true, as a weaker signal might reduce your available bandwidth. But the data stream bitrate is controlled at the server end, with the provider usually using something called adaptive bitrate. It determines the maximum rate your device can accept based on the number of error packets it receives back from the device. Longer distances will usually increase the error rate, which in turn would tell the server to stream at a lower rate.
Nothing of course is set in stone, and this would only be a generalization. But overall it should hold pretty true in real life use.
Dan
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