Does CyanogenMod support the Google Play Store and Google Account integration? As it says. I am looking into CyanogenMod as a stopgap measure before I upgrade to an iPhone this year or the next. My current phone no longer gets updated and I cannot justify having year old bugs still active.

However, I have invested quite a bit of time in my current Android ecosystem and I both do not want to ditch that AND I want to be able to easily transfer my apps to the iPhone when I am setting the latter up, through the Apple transfer app. Are both an option when using CyanogenMod in this manner?
On a custom Os like Cyanogenmod you must flash the googleapps.zip from the recovery. The apps and services aren't built in but are very easy to flash.