Grimrods often throttle back an inboard whilst doing a LL patrol or SAR sortie over the sea- this does save fuel, but I believe it's more to do with having instant(ish) throttle response in the event of having to climb away fast, since they are so over-powered they would have to be throttled back a long way on all 4, with the associated spool-up time.
3-engine take-offs are perfectly possible. We do them as a matter of course in Albert (simulated in the aircraft, or real in the sim) - it is a basic training requirement. Plenty have been done for real as well.
16B