Grumpy_Mike:
Yes what could happen is the chip could oscillate and generate interference. Current draw would increase but only to what it could be if fed with those fast signals.
It can potentially be damaging, if the input spends too long at the threshold.
From the Texas Instruments application note SCBA004D, "Implications of Slow or Floating CMOS Inputs":-
.....causing the N-channel and the Pchannel to turn on simultaneously, generating a current path between VCC and GND. This current surge can be damaging, depending on the length of time that the input is in the threshold region
Doesn't mean it will happen, but it can.