It depends on the setup. In most cases, the waterfall feature will circulate the pool water not the hot tub water, why would you want hot water go into the pool.

Our pool (put in by previous owners) does lose heated water because it just spills the hot water over the top. As a result, we only heat the hot tub when we have the spillover off. We hate, hate, hate the built in hot tub because it is so useless. We would much rather have just a water feature. We actually bought a freestanding hot tub. It has more jets, doesn’t have the annoying spillover issue. It is all around better.

Thanks GN Builders and smit2380. I just grabbed the above picture off line, but I have definitely seen integrated hot tubs that seem to spill over in a waterfall and appear to dump right into the larger pool. I'm asking because this set-up doesn't really make sense to me. We'd need a propane tank to heat the pool and tub and expect you'd burn through propane like crazy with this feature.

...and thanks smit2380...it makes sense that you can shut off the "spillover feature".