With Great Britain in firm control of the Straight of Gibraltar, there was no way they were going to get home. So the next best thing was to arrange a flag transfer to the Ottoman Empire in the manner you described.
While you are right about most of the Ottoman's fleet being out of date, the sheer numbers were impressive enough to:
The Russian ships weren’t much better than the Turks, and totally outclassed by the Goeben, which was an honest-to-goodness post-Dreadnaught BC. Any attempt for a Russian BB to shoot it out with Goeben would have been suicide.
But yes, the Ottomans did okay.