Even at the time of the Microsoft deal in 2011, Nokia hadn't been US-focused for at least 5 years. US carriers weren't carrying any Nokias beyond the $50 dumbphones you could get anywhere. Unlike the rest of the world where people bought phones at more or less full price, the US market had mostly carrier subsidized pricing, and carriers ran the ad campaigns, not manufacturers (except Apple).
Back when the iPhone, HTC G1 and Motorola Droid ads were saturating TV around 2008/9, I couldn't recall seeing a single ad for Nokia. Nokia's only real sales outlet were 3(!) retail stores in the entire US. And even those shuttered well before 2011.
The idea that focusing away from the US might have saved them as an independent entity doesn't hold up because their average selling price (ASP) was falling due to low-end models selling better than their more expensive smartphone line. Eventually it reached a turning point where the brand was more closely associated with super-durable and super cheap "burner" phones than upscale smartphones.
Finally, their smartphone line was a mess because like Windows Mobile 6.x, the OS appeared on a variety of screens, both touch and non-touch. The Ovi app store was deeply fragmented as a result, because old apps scaled badly on larger touch devices, and newer apps didn't work at all on the non-touch phones.