Connecting condensate pump to sewer
Yes, you can plumb the outlet of the condensate pump into the tailpiece of the shower. Assuming the condensate line is properly trapped, then there should be no problem. 

You'll notice in the code snippet below, that it says "If discharged into the drainage system, equipment shall drain by means of an indirect waste pipe.". Which means you cannot, plumb the condensate drain directly into an untrapped waste line or vent.  


  Uniform Plumbing Code
  
  Chapter 8 Indirect Wastes
  
  814.0 Condensate Wastes and Control.
  
  814.1 Condensate Disposal. Condensate from air
  washers, air-cooling coils, fuel-burning condensing
  appliances, the overflow from evaporative coolers,
  and similar water-supplied equipment or similar air-conditioning
  equipment shall be collected and
  discharged to an approved plumbing fixture or
  disposal area. If discharged into the drainage system,
  equipment shall drain by means of an indirect waste
  pipe. The waste pipe shall have a slope of not less
  than one-eighth (1/8) inch per foot (10.4 mm / m) or 1
  percent slope and shall be of approved
  corrosion-resistant material not smaller than the
  outlet size as required in Table 8-2 for air-cooling
  coils or condensing fuel-burning appliances, respectively.
  Condensate or wastewater shall not drain
  over a public way. 
  
  814.3 Point of Discharge. Air-conditioning condensate
  waste pipes shall connect indirectly to the
  drainage system through an airgap or airbreak to a
  properly trapped and vented receptors dry wells,
  leach pits, or the tailpiece of plumbing fixtures. 
  Condensate waste shall not drain over a public
  way. 
  
  Chapter 2 Definitions
  
  211.0  -I-
  
  Indirect Waste Pipe - A pipe that does not connect
  directly with the drainage system but conveys liquid
  wastes by discharging into a plumbing fixture, interceptor,
  or receptacle that is directly connected to the
  drainage system. 
  
  222.0 -T-
  
  Tailpiece - The pipe or tubing that connects the
  outlet of a plumbing fixture to a trap. 


So you could have something like this, with the condensate pump.



If you can maintain the proper slope, you could remove the condensate pump.



In this situation the condensate pump is not required, since the tailpiece of the shower serves as the air gap. And you won't have problems with sewer gas, since the drain is protected by the trap on the shower drain.

You'll want to use proper fittings to connect to the tailpiece, rather than hacking together some leaking contraption.  Without knowing the size and material of the condensate drain, I can't tell you exactly what fittings to use. In the end, you should end up with something like this.



You'll cut the tailpiece, and fit in a new 45&deg; wye. Then you'll use whatever adapters and reducers are required, to go from the condensate drain into the PVC wye. The condensate drain has to maintain the minimum slope, so you'll have to work with that as a constraint.