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The GA code is just normal javascript, there is nothing special about it, there should be no conflict. I use GA and it works fine -- I put the code (asynchronous version, of course) in a chunk and then include that chunk in my templates above the </head> tag. Works fine. It should also work to put it directly in the template, or put it in a TV and put that in the template (but why do it that way, Jason, do you want to have different GA code on different resources for some reason?).
I bet your anomalies arise from your use of iframes, not from MODx per se. Iframes break Google's basic model of the internet, which can have unexpected results both in GA and in search. Google wants everything to have a unique URL. Using an iframe sort of combines two URLs into one "page". For purposes of search, Google regards an iframe as similar to a link. GA treats an iframe as a separate "pageview" because when you load the new URL into the iframe, it calls the JS tracking code for that URL.
I'm not clear on what you mean by "strange data numbers" but I would have a look at exactly how the data is being reported, decide whether you want the iframe "pageviews" to count as a separate pageview in GA, and remove the GA code from the iframed content if you don't want that.