Yes, Remington sewing machines were made by the same company famous for firearms. Sewing machines were manufactured during the 1870s and 1880s at the Remington foundry in Ilion, New York. According to Carter Bays, in his Encyclopedia of Early American Sewing Machines, attachments for Remington machines were embossed "The sewing machine like the rifle gun, that beats the world is the Remington".
Here's an imaginative marketing image - a sprite riding a sewing machine on a butterfly!
And another fantastical image: a sewing machine serving as a howdah on the back of an elephant. Remington machines were manufactured as treadle or hand-crank machines. The image in the lower right corner depicts a hand-crank machine; note the feet that support the machine base - they're often referred to as paw feet.