Do the JTAG pins have a weak pull-up/pull-down resistor when these pins are reserved for this function?
The weak pull-up/pull-down is not enabled when the JTAG function is implemented. The I/Os are simply 3-stated; therefore, it is advisable to implement a weak pull-up/pull-down resistor in your design. This will prevent the JTAG inputs from floating, which eliminates the chance that the CoolRunner would draw higher currents from the power supply.
NOTE: The other 3-stated I/Os, by default, retain their weak pull-up/pull-down implementation as allowed by the features of that part.