Do birdhouse gourds and squash cross-pollinate?

Is there any risk that seeds  of pumkins selected from a garden that also grows birdhouse squash giving bitter fruit? (not hand-pollinated)

I asked a similar question earlier this year and the answers could help you.  Birdhouse gourd and cross pollination with other squash?

You'd need to know the species of the pumpkin, or it might be easier to just research if any pumpkin could be in the same family as the gourds.  (sorry if I'm getting my family/species/phylum terminology mixed up)