Being in the same alliance isn't necessarily the only test. I'd phone both UA and Icelandair to see if there's an agreement for the transfer of bags. You'll have to show your complete itinerary when you check-in with UA. Also be sure to ask if UA can issue your Icelandair boarding pass, unless you can get it online. We once flew from DCA to MIA on AA then on to GRU on TAM, using two separately purchased tickets (latter flight was through Priceline). At DCA, AA was able to give tag our bags all the way to GRU, but could not issue our TAM boarding passes, so we had to stand in line at the TAM counter at MIA to get those. When you phone you can find the gate numbers used.