A urethane is the O-C(=O)-N functional group (also called a carbamate). Since you have added another carbonyl to that, it's not going to behave like a normal urethane. The properties would probably be a lot different, and I would guess that would be in a bad way because you have increased the possibility of hydrolysis of the carbamate or ester.
In terms of reactivity, however, I am pretty sure that the reaction would occur as you have drawn, but isolation might be difficult in the presence of water.