I don't see why it would. If I were you, though, I'd change the headers for the redirect instead of using a meta refresh, if you can. It is just better this way; plus some browsers have the meta refresh feature disabled.

This can be detected by the search engines. Your concern is that it does not look like you are linking to your own site.

Often this sort of "fear of google" is beyond what is necessary. Yes - a cross link is not in and of itself good - but if it is right for your business - it is right for your business. Period. Don't let what Google might or might not do decide what you offer to your users. Ultimately the focus on your users will better serve you with Google as well.

On the re-direct itself - even setting the Meta tag to zero does not result in an instantaneous transfer - it still delays a full second on the landing page. You are better off re-directing on the server if you really want to re-direct -- though again - the search engines can easily detect this.

So best solution - fastest for the user - is a good old direct link - it may be the right way to do.

geordief, is it the case that the external site you're linking to is a site with which you have a referral/affiliate relationship? If so, are there LOTS of links from your site to this other site, i.e., a majority of the external links from your site? And are there many other external links to other sites, and are those links direct?

META Refreshes - Don't Go There!
With the exception of refreshing, for example, a 404 page to another page, I would strongly recommend against using META refreshes. For years META refreshes were widely abused, commonly refreshing a "doorway" page to other site pages intended more for conversion. This is an old-school version of what the engines refer to as "sneaky redirects." Google recommends against their use, undoubtedly because the presence of META refreshes, and especially the widespread presence of them, probably now is used as a spam indicator.

On the re-direct itself - even setting the Meta tag to zero does not result in an instantaneous transfer - it still delays a full second on the landing page.

Just as an FYI, that statement is not correct. A meta refresh set to "0" does indeed yield an instantaneous refresh.

Preferred Redirect Methods
You could instead run the links through JS and count them that way. You could also run them through a robots.txt protected directory so the links can't be seen or followed, which is what I'd do.

Lastly there is the option of simply adding a nofollow to the links themselves. I hate nofollow at the link level and won't use it except in rare cases, but it is an option.