I don't think that is correct!
Conversion is the amount of starting material that has reacted, regardless of what product it goes to. So in that example, you would have 20% conversion.
Yield is the percentage of theoretical maximum for each product, so if you isolate 10% of your material as your desired product, it's 10% yield. If you account for the rest of the converted material as another product in 10% yield, then you got 10% yield of each of those.
What you described as yield of desired product/% conversion is sometimes called "yield based on recovered starting material." I think that this term is overused, however, and I think it's a bit disingenuous to report a reaction like you described as "50% yield based on recovered starting material" unless you also state the actual chemical yield of that step (10%). It's just misleading to say that you could get 50% yield when you would have to run that reaction more than 5 times to actually get 50% isolated yield.