My thought: emphatically, no.
That doesn’t mean the tagline can’t accompany your logo, and you can even make it look as if it’s a single element in selected cases.
But please reserve the right to separate them and use the logo as a stand-alone element where necessary. I blogged about the logo standing out when grouped with other logos – Does your logo stand out? It just won’t stand out if must carry along a tagline.
For my own company logo, I integrate logo and tagline where I have a full line devoted to the two elements, but elsewhere I separate them and usually only use the logo itself. Below are examples.
First, logo and tagline associated:
Then the logo alone:
So, logo and tagline are separate elements that can be integrated as appropriate. The thing is, be sure you have the flexibility to do either.