Well, from what we see in the Inuyasha series, no. Sesshomaru is often portrayed as aloof and disdainful towards humans, while Kagome is a human girl. Her bond is with Inuyasha. Sesshomaru is more focused on his own journey of self - discovery and power - seeking. There are no real signs or plot developments to suggest a love story between them.
In the original Inuyasha series, it is highly unlikely. Sesshomaru has his own character arc and goals mainly centered around power and his own pride. Kagome is in love with Inuyasha. Their storylines don't really lead to a romantic connection between Sesshomaru and Kagome.