Checking baggage through to final destination

Just need to be sure on this: If VS sell you a ticket to one of their destinations with onward flight with another airline to final destination, they'll be happy to check your luggage through to final destination? If you source the other flight yourself they won't?
Am keen to be clear on this as we're flying LHR-LAX-PSP in a few weeks and, although VS said they could through ticket us (the LAX-PSP sector is on UA) the cost was considerably more than buying the second sector direct from UA. In a nutshell, I'm assuming we won't be able to dump our bags at the transfer luggage drop off point just after Customs & will need to take them over to UA at T8?
Thanks,
James
Am keen to be clear on this as we're flying LHR-LAX-PSP in a few weeks and, although VS said they could through ticket us (the LAX-PSP sector is on UA) the cost was considerably more than buying the second sector direct from UA. In a nutshell, I'm assuming we won't be able to dump our bags at the transfer luggage drop off point just after Customs & will need to take them over to UA at T8?
Thanks,
James