Is it necessary to check for Rahu Kaalam (inauspicious time) when starting the Thirumanjanam for the Saligrama Perumal? 

If starting the Tiruvaradhanam for the very first time now, one may start at a time other than Rahu Kaalam. Otherwise, since Perumal Tiruvaradhanam is a daily service (Nithyapadi Kainkaryam) and a daily ritual (Nithyanushtanam), there is no necessity to check for things like Rahu Kaalam.