At first glance, no. However, if you read the poem carefully, three main allusions stand out. The first two are the allusions to Death and Immortality, certainly allusions to the bible and to biblical allegory. Death is personified as the driver of the carriage, and Immortality is along for the ride, a shadowy figure at best. Both of these images, along with the idea of eternity expressed at the end of the poem, are clearly biblical.
Another allusion is the overall metaphor of the poem – Death as a carriage driver, with the horses’ heads turned toward immortality. This could evoke the idea of the four horsemen of the apocalypse, also found in the Bible. It seems that Dickinson’s carriage driver is a far less threatening image, designed to comfort rather than terrify. Though Emily Dickinson is not giving the reader any obvious allusions here, these three images are bound to resonate in the hearts of the Christians of her day.