I have done this route about 8 times with BA/IB and yes, your luggage will definitely be checked through on to the IB service. Same on the return leg. This would also extend to it being checked through on to Binter Canarias if you were doing an inter-island hop once you arrived in the Canaries.
I have never had any problem with my luggage on these routes ex LHR to the Canaries with BA/IB.
However, what you will have trouble doing (unless it has changed in the past month or so) is choosing your seat (if this bothers you at all).
The integration between BA and IB is still very disjointed in this respect and will only allow you to choose your seat with the carrier you booked your ticket with, so much so that to guarantee my chosen seat with BA, I had to pay 12 EUR per passenger, as the system would not allow you to do this even 24 hours before through online check in - even with a BA booking reference.
So much for free choice of seat upon online check-in...