OP, short answer, no.
All CC applications for new products will be subject to a HP, regardless of whether you are pre-approved and/or an existing customer.
This. Sorry OP don't see this happening.
OP, as others have mentioned...it's probably not going to happen with BoA. I've been a customer with them for over 20 years and at one point had 4 of their cards....all of them were HPs. The only major I was ever approved for on a SP was Discover and trust me, I was shocked.