This is how your routing looks like:
http://www.gcmap.com/mapui?P=yvr-fra-ath-lhr-nrt-yvr
Of course this is permitted. The only issue is that you are leaving a lot of miles wasted. A normal RTW can do 29,000 miles, (26k for the Y special) but you are only using 18k. So there are a lot more places you could fit into your itinerary. Ever wanted to go to New Zealand? Hawaii? Guam? Spain?