Nope. On traditional PalmOS it saved state but was essentially single tasking. Because the apps were so small and data minimal you didn't really need multitasking, just the impression of multitasking was enough to be productive. Later on they merged BeOS into PalmOS but IIRC Palm never shipped a product with that version.

Symbian was proper multitasking with no state saves. What it did do differently was ask you to close apps if it ran out of ram or didn't have enough to start an app which it did frequently on Nokia phones. That's why you had to pick carefully with Nokia so you got 'Hero' devices like the e71 or n95-2 which had more ram than crap like the 5230. Every now and again Nokia would let one slip out.