No. Howrah-Madras was introduced several decades after Howrah-Chennai Mail ( Mail started in 1900, this train started after the 50's), and Coromandel was a completely different train. There used to be one Howrah-Madras express and one Madras-Howrah Janata express that used to run alongside the mail. The Janata was cancelled and in it's place, a Howrah-Tirupati service was started, while the Howrah-Madras express was cancelled/diverted and Tatanagar-Madras was started. Quite a few people have said the same in the IRFCA message archives. Sharing the link to one such discussion below, refer to the post by Mr. Sankaran Kumar:
click here