Generally speaking, yes. "Crashing" a process will not cause recent memory writes to be lost.
From the point of view of the CPU, raising an exception is used just as often for "normal" events as it is for fatal ones. For instance, accessing an unmapped page of memory does not always cause a crash by way of GPF/SEGV; many operating systems will use this event to implement dynamic memory paging (e.g, reading in pages of a memory-mapped file; allocating physical memory for a zero-fill memory region; copying COW memory pages). Similarly, other CPU exceptions, such as software interrupts or software-emulated instructions, may be interpreted by the operating system and passed back to the process without killing it.
(Also: consider the cases of core dump generation and debuggers. A process that is killed is not always destroyed immediately; the operating system may retain its state in memory for various purposes.)
Most operating systems will either flush the cache on a context switch, or will allow the CPU to write out pages from the cache normally. In either case, recent writes will certainly not be ignored.
