Are you sure it's white spruce? That is a cold-climate tree and can have difficulty even in z6 (too warm), let alone z10. I'd look for something else.

I'm not qualified to speak to the suitability or lack thereof of 'weeping white spruce', at least not beyond what Ben already said.

If you can get your hands on a morinda spruce, that would seem likely more suitable for LA. (Deodar cedars come from a similar climate, and grow just fine there) It's considered 'weeping' too.

UPDATE: Didn't have time to find the reference this morning, but Jacobson's NALT reported a 58' Picea smithiana in Sacramento. So it could certainly handle the climate of most of the LA basin.