I would say absolutely yes. I started with the STM32 parts and have then used ARM Cortex devices from TI, Freescale, and Atmel. They all have different peripherals and of course different peripheral libraries from the vendor but overall they are conceptually similar. It can certainly be a pain in the neck to switch a project from one device to another (lots of gotchas with pin layout, peripheral minutiae etc etc) but starting a new project with a different device should not be too hard!

Except for the Kinetis DMA, I never understood that one!!