That’s an intriguing idea! However, while I can see Delia perhaps wanting to start a relationship, Byakuren not as much. He’s a thousands of years old dragon god and in general not really the romantic type. There are even jokes that he just had Yellow through osmosis or something since he never speaks about her other parent. But, while I don’t think they’d end up together romantically, I can see them being good friends! I haven’t thought as much about the dynamic between all the ‘Pallet Parents’ aside from the Charlie/Aiden/Scarlett/Byakuren childhood friend quartet, but since Delia lives there too I’m sure she’s part of that friend group.
I can see her being especially close with Scarlett (Red & Leaf’s mother) and Sylvie (Chase & Elaine’s mother) in a sort of ‘Pallet Town Mom Friends’ group, but I’m sure she’d get to know Byakuren as well. I’m not sure how much he sticks around after Yellow grows up – if he stays in Pallet or heads back to his home/domain of Viridian Forest – but either way he and Delia definitely know each other and are probably friends! Byakuren can be kind of prickly around people who aren’t his immediate friend group, but Delia is also very open and persistent so if she decided she wanted to be friends with him she’d probably manage it. Since she would have known Aiden and Charlie growing up (all three of them being raised in Pallet, and doing a bit of math – she’d be maybe a year or two younger than them), she probably would want to get to know their mysterious new dragon friend as well. As such, they’ve probably known each other since Delia was a teenager, so plenty of time to become friends. Both raising their kids on their own as well, they likely helped each other out with parenting (of course Aiden, Scarlett, and Charlie helped out as well), especially since Delia was quite young when she had Ash.
Ash and Yellow would have grown up as childhood friends. Ash would be around three years older, and they’re both very sweet and friendly people so I can see them spending time together when they were kids aside from just hanging out since their parents are friends. As they’re both only children, perhaps they already had a sibling-like relationship where Yellow looked up to him as an older brother figure (though it was generally Red who was more overt with seeing Ash as a brother figure.) I’m sure they keep in touch as adults since both seem the type to want to stay up to date with their childhood friends, but since they live in different regions now they likely don’t see each other as much unless Ash and his family are visiting his hometown (for the holidays or something.)
So, while I can’t see a ship between their parents working out, Ash and Yellow are still close friends!