Not necessarily. As was explained already, they have different audiences and appeal for different reasons. There is no reason to assume a Muppets TV show would be a success just because Sesame Street is.
I think there is every reason to believe that because Sesame Street is still popular a new Muppet Show would be too. Those of us old enough to have been a kid when the Muppet Show debuted (ahem) know first hand that the reason we watched in the first place was because Kermit was on it. For us, it was Sesame Street that was on around our bedtime. Heck, even the second episode of the Muppet Show had a "guest appearnce" by Ernie and Bert to help solidify that cross-over audience. When it started, The Muppet Show heavily leveraged the Sesame Street brand to get itself established.
I think it would happen again. The kids watching Sesame Street now don't now the Muppet Show at all. They would watch it because its like Sesame Street, which they do know. Also, their parents would probably get them to watch too (as mine did) because parents like Sesame Street and they also likely remember The Muppet Show with some fondness.
I'm tellin' ya, it would work!
Of couirse, the whole above argument is predicated on the notion that Sesame Street is still really popular. I wonder if that's still true? It was one of the only decent kids shows on in the 70's. Now there's tons. Whole channels are devoted to pre-school programming, 24x7. So, I wonder.