searching for nectar and pollen 不是定语,而是伴随状语,也就是与谓语动词 visit 同时发生的伴随行为,即它们一边 visit flowers 一边 searching for nectar and polle.这个句子也可以改为——
并列谓语：They are able to visit dozens or hundreds of flowers in one day and search for nectar and pollen.
while引导的从句：They are able to visit dozens or hundreds of flowers in one day while they are searching for nectar and pollen.
可以这样翻译：
1、它们在一天内能够飞临数十朵或者上百朵花寻觅花蜜和花粉.
2、在采集花蜜和花粉的同时,它们在一天中能够造访数十朵或者上百朵花.