No. They’re Just Puppets.
Sesame Workshop President and CEO Gary Knell, wrote in the book Sesame Street: A Celebration of 40 Years of Life on the Street, “They are not gay, they are not straight, they are puppets. They don’t exist below the waist.”
I always just assumed they were brothers. Same room, separate beds. Bert’s the older one, essentially a young adult, and Ernie’s the younger brother. They were originally going to have them be father and son except they didn’t want to encourage kids causing trouble for their parents.