The company I work for specifically directs that engine anti-ice be on during live (engines on) deicing. The logic behind this is that any deicing fluid spray that inadvertantly enter the engine may cause blead contamination, but by using engine anti-ice it is purged out through that system and with the bleeds off the likelihood of bleed system contamination is very low. This reduces the chances of air conditioning system contamination and problems after takeoff with cabin air quality.