Outcome when logic output of IC shorts to VCC
Philips NXP Nexperia has the HC(T) User Guide, which shows in figure 33 what happens when you overload an output:



So the outputs will not go above a certain current. But it's still too high.

This shows typcial values, not the possible maximum, but even so it certainly exceeds the IO limit of 25&nbsp;mA that can immediately damage the chip.

Actually, this graph is for 4.5&nbsp;V. There is another graph for 2&nbsp;V, where the current stays below 10&nbsp;mA, so you have to measure what happens at&nbsp;3.3 V.

Anyway, the guide says in section 8.2:


  The maximum rated DC current for a standard output is
  25&nbsp;mA and that for a bus-driver output is 35&nbsp;mA. These
  ratings are dictated by the current capability of on-chip
  metal traces and long-term aluminium migration, but it is
  expected that output currents during switching transients
  will, at times, exceed the maximum ratings.
  
  A shorted output will also cause the maximum DC current
  rating to be exceeded. However, one output may be
  shorted for up to 5&nbsp;s without causing any direct damage to
  the IC.
  
  The life of the IC will not be shortened if not more than one
  input or output at a time is forced to GND or VCC during
  in-circuit logic testing (“back drive”) as long as the following
  rules are obeyed:
  
  
  maximum duration : 1&nbsp;ms
  maximum duty factor : 10&nbsp;%
  maximum VCC : 6&nbsp;V
  


Please note that shorting an output for 5&nbsp;s will not cause "any direct damage", but this implies that there will be indirect damage that will shorten the life of the IC. To avoid that, you'd have to keep the duration of the short below 1&nbsp;ms.