In principle: Yes, if program execution moves from one core to the next, it might not see all writes that occurred on the previous core.
Keep in mind though that processes don't switch cores by themselves. It is the operating system that preempts execution and moves the thread to a new core. Thus it is also the operating system's responsibility to ensure that memory operations are properly synchronized when performing a context switch.
For you as a programmer this means that, as long as you are not trying work on a level where there is no SMP-aware OS (for instance, when you are trying to write your own OS or when working on an embedded platform without a fully-fledged OS), you do not need to worry about synchronization issues for this case.