Rubbish! The CPU isn't the power hog that you think it is in smartphones, nor are the programming techniques. Things like the screen and the radio consume most of the power.
For most use-cases, yes, but there are some CPU-intensive (usually graphic-intensive, so maybe GPU-intensive) processes that will eat up your phone's battery life like crazy. I mostly find this in games--Ingress is the worst offender I've dealt with, but Kingdom Rush (which uses no GPS or radio) drained battery much more quickly than just having my screen on for, e.g., reading.