Does length of wire to NFC antenna affect ability to read tags?
Even coaxial cable will have some attenuation, and although it may not be huge, it still subtracts from the link power budget.

Just how much it will subtract depends on the specific type of cable used (there are other things involved, but in this context it comes down to the cable alone), but the short answer is that any added length of connecting cable from the antenna to the actual receiver or transmitter will reduce the effective range of the system when viewed from an antenna to antenna perspective.

Whether the change in effective range is noticeable will depend on the characteristics of the cable, and will go from indiscernible to noticeable (coax varies widely in attenuation characteristics depending on the specific one used).