Can I use a split tab switch for mains voltage and low voltage?
This is OK provided that the wires to the fan control switch are treated as 120VAC wires as per 725.46:


  Class 1 Circuit Wiring Methods. Class I circuits shall be installed in 
  accordance with Part I of Article 300 and with the wiring methods from the 
  appropriate articles in Chapter 3.


(i.e. run using NM and not communications-type cable/wire) and as per 725.48(B)(1):


  (B) Class 1 Circuits with Power-Supply Circuits. Class 1 circuits shall be 
  permitted to be installed with power-supply conductors as specified in 
  725.48(B)(1) through (B)(4).
  
  (1) In a Cable, Enclosure, or Raceway. Class 1 circuits and power-supply 
  circuits shall be permitted to occupy the same cable, enclosure, or raceway only
  where the equipment powered is functionally associated.


since the control wires are with the fan's power wires, and we can safely treat them as a Class 1 control circuit using the provisions of 725.130, Exception 2:


  Exception No.2: Class 2 and Class 3 circuits shall be permitted to be 
  reclassified and installed as Class 1 circuits if the Class 2 and Class 3 
  markings required in 725.124 are eliminated and the entire circuit is 
  installed using the wiring methods and materials in accordance with Part II,
  Class 1 circuits.