I'm not absolutely sure what you're asking, but if you are thinking about having an identical h2 on every page I would strongly advise against it, and generally you should ensure that h tags make semantic sense (see e.g. [w3.org ]).
The h tags form part of the semantic construction of the page (they have a content-related meaning), but it sounds as if you want to use them for presentation: best practice is to keep content and presentation separate.
Tonearm. This is very unlikely to be helpful, as h2 headings don't work that way. Heading tags aren't magic bullets that boost rankings of the words they contain. I think that well-structured pages are rewarded, at least in helping Google understand what the page is about... and unique and relevant headings on a per page basis can be worth some effort... but each heading would need to fit into the unique "outline" structure of its particular page.
A global slogan in an h2 tag, though, couldn't possibly contribute to the understanding of very many pages on a site, if any at all. It's necessary to think through where an h2 heading fits into a page's structure to get this point. As Wilburforce puts it: "you should ensure that h tags make semantic sense".
Additionally, Google might well notice the global addition of an h2, particularly if the slogan is very long and the h2 was out of place (which it seems it would be), and a spammy intent would be clear. Hard to say how much of a negative effect this would have... but it's not likely to help.
Also, somewhere in the early roll out of Penguin, I vaguely remember some statement from Google about keyword lists being the type of onpage spam signals they'd be looking for... and I think I've seen at least one site where a "slogan" that grew to include too many keywords has hurt. Probably depends on how long the slogan is, how badly "stuffed" it is, and how clean the site was otherwise.
I agree with Robert this is an issue of semantics and not that relevant to SEO.
Under good old content focused HTML 4.x this heading would not make sense as it is not part of the subject heading <h1>.
Under stricter document focused XHTML this would be very acceptable as the sites logo would be <h1> and this <h2> would form part of the page structure along with the sites title under another <h2> (nasty but its W3C donít blame me!)
Under HTML5 that brings both together and make things perfect, your slogan would be under say <footer> or <aside> but under <section> and start with a <h1>. Remember your article will be enclosed in an <article> tag that contains another <h1> for the title of the article.
Anyway Google will probably filter it out so whatever your coding style will not likely to help in the SERPs.