As others have said, most modern transmission technologies are pretty deterministic, and a string of X bits will always take the same time to transmit, either as is, or if a lower layer requires scrambling, but applying a fixed ratio.
There are however a few cases when there could be a slight effect, if some characters need to be escaped. This is for instance the case for PPP, where at least
0x7E need to be escaped (the former being the escape prefix, and the latter being the frame delimiter). Additional characters may need to be escaped if the link requires it. For those characters, it will take twice the time to transmit them. Since PPP is still the basis for PPPoA and PPPoE and used in some last-mile scenarios, this could have a very slight effect. Unless of course your file is just a repetition of
0x7E, in which case it will take double the time compared to a file not containing those characters at all.
There is also the case of bit stuffing as used for instance by HDLC and USB: the NRZI coding scheme does not change level when series of ones are sent, so after too many ones, a zero is inserted to make sure sync is not lost. Worst case here is that if you send only ones (i.e. your file is just a repetition of
0xFF), then it will take 20% longer (HDLC, extra bit after 5 ones) or 17% longer (USB, extra bit after 6 ones) than if you send all zeroes or any sequence that never includes a 5- or 6-bit sequence of ones.
Back in the old days when not all links where 8-bit transparent, data transmitted could need encoding in some situations (e.g. base64 for binary data) and not others (e.g. pure ASCII sent as-is), with stuff like quoted-printable in between (e.g. text with a few accented characters). So depending on what you sent, it would require more or less characters/bits on the wire. But that should be extremely rare nowadays (and was mostly an issue for mail).
In all those cases, it's not really the entropy that matters, but the actual content matching specific sequences. If you have high entropy data (e.g. compressed or encrypted data) then you get a relatively consistent average speed even in those cases. If you have specific sequences of data (you send 1 GB of
0x7D over PPP or 1 GB of
0xFF over HDLC for instance), then it could take longer. If you avoid those sequences altogether, it could be shorter.
Note that some lower layers introduce compression even if you don't use it at higher layers. Again, back in the old days of POTS (dial-up) modems, the modems could use V.42bis compression between them. There are probably a few other transmission technologies which include compression at a relatively low layer.