Whether or not it could make sense depends, like always, on design and purpose. No it doesn’t make sense if you make it like you would make a sinew-backed bow and just supplant the sinew with bamboo.
To evaluate when it makes sense, you need to look at the particular properties of the materials you are working with, and make them work together for the purpose you’re after. It’s a bit like the comment Saxton Pope gave on the Bari-tribe’s black palm longbow: for the conditions the Bari are used to shooting in (extreme moisture, dense forests requiring long arrows, shooting vertically most of the time), it’s a superior design, but Saxton Pope thought these bows were crap, because he looked at it from his own perspective only.
If a particular bow design has survived hundreds of years, there’s probably a reason it’s still there. If we think it's crap, its probably because we haven’t understood it yet.
If you have a not-so-elastic backing like bamboo, but which is very strong (high Modulus of Elasticity), you can add a horn belly, which is very elastic (in compression) but has a low MOE. The result is a bow with the neutral plane very close to the back of the bow. The back is not strained (stretched) a lot but due to its high MOE it still takes a lot of stress. In reverse, the belly is strained a lot (compressed), but due to its low MOE it isn’t stressed to its max. The stress-strain combo of both materials, however, can be combined so that both are perfectly in balance.
Basically, this is what PatM's been saying from the beginning of this thread.
Sure, the horn isn’t used to its full potential, but neither is sinew on a bow without a horn belly. I did some calculations on strain levels on turkish and korean bows. There, both back and belly are strained about 5%, which is about optimal for both materials (in terms of energy storage). In sinew-backed native american bows, the sinew is hardly ever strained more than 2.5%, so the sinew is never really put to the test. Are these bow therefore slow? No, as mass placement is more important than mass itself.