With the Tac!t cable, current draw is necessary for the circuit to operate: the device will not work with dynamic microphones that do not pull current.
The actual current draw varies with the load used, so it's not possible to provide a specification for it. The circuit demands are very low, and with IEC 26815 compliant P48 supplies it is very unlikely to cause any problems.
With excessively hungry microphones (e.g. those that suggest they need the full 10mA available, such as Earthworks), or phantom powering that cannot deliver adequate current (or is significantly under-voltage), you might start to encounter a few problems. The likely outcomes in such cases are under-performance of the microphone in terms of max SPL etc., or a slight increase in self-noise.
Tac!T can stack with internal mixer filters to create a dual slope HPF, but perhaps has its greatest value in applications such as camera inputs where no HPF option is provided.