I launched my UK based store late October last year, and while we haven't had a strong SEO strategy, I have seen us rank for certian terms as the weeks go by.
We very quickly ranked for the name of the store and got to the top 3 in Google, but that's not suprising as there isn't much competition.
I check my site on SEM Rush, and every so often we start to rank for some additional keywords, and they slowy rise through the ranks, from page 10, to 9, to 8, etc.
We have a few keywords that are ranking on pages 2 and 3 of google, but nothing in the top 3 results, but as I said we haven't had an SEO strategy, just tried to follow some good practice.
I have noticed that we are ranking for a lot more terms in the states than in the UK, so it's interesting to know that may be due to the server location, but that suprises me as most companies don't use their own servers, so sites could be hosted anywhere.
I hope that gives you a little insight on our experience. Good luck.