Cloud vaults - query

I have a vault on a home pc, and one on an external drive. When I use my phone away from home to get full quality pictures it can take a bit of time as my upload at home is only 2mbps. So I’m wondering if I add a cloud vault will my mobile in this example download photos from there hence be faster?

Also is one of the cloud providers preferred? Ie one that works best?

Cheers

Mark