From SP.16 ,737 FCOM :
Use wing AI ,during all ground operations between engine start and take off when icing conditions exist or are anticipated,unless the airplane is,or will be protected by use of type 2 or type 4 fluid in complance with an approved ground de-iceing program.
Warning: do not use wing anti-ice as an alternative for ground de-iceing/anti-icing.Close inspection is still needed to insure that no frost,snow or ice is adhering to the wing,LE devices,stabilizer,control surfaces or any other critical aircraft components at take-off.
I very much doubt that any company will,for some reason decide not to follow this.
One big problem with taking off with 'some' ice on the wings is the chance of not symetrical icing of both wings,and you'll be amased how fast you'll do a barrel roll,even with a heavier airplane.It's just aerodinamics.
And ,unfortunately ,it happened already,so you better learn from their death.