I have seen claims that adding conformal tanks reduces drag. With all due respect, I find those slightly unlikely. However, it might be true at the new sortie profiles now being demanded. More likely, what they are actually saying is that a set of conformal tanks generate less drag than the equivalent set of drop tanks. That would be very likely. Conformal tanks usually appear toward the end of an aircraft's service life. Perhaps driven by the 'in-service' factors I outlined above. Sometimes, they appear during development - the V-22's external fuselage fairings grew massively during development to house more fuel as they struggled with weight increases.
Engines, according to those in the know (which I'm not), at least on the F-15 the conformal tanks resulted in no increase in airframe drag when subsonic, although transonic/supersonic was a different story (never heard anyone claim a reduction though). Looking at the installation, my aero engineer training says the claim is at least plausible as it gives the aircraft a more 'tear drop' profile.
I've not heard much about the F-18 conformal tank installation, but I'd expect similar results (especially since it's coming from the same people).