Short answer is yes. Driving the gearbox loads - be it hydraulics, big electrical generators, or something else - take energy from the core of the engine and hence increase fuel burn.
Part of the thinking that went into the no-bleed architecture of the 787 was that - by not having to account for high pressure bleed air from the core - the core could be better optimized and hence for fuel efficient. But it didn't really pan out that way - in fact the GEnx-2B engine on the 747-8 uses the same high pressure core as the GEnx-1B engine on the 787 - even though the -2B has conventional engine bleed to run the packs.