It won't affect it however, if you're able to wait until he receives his Canadian PR, I would recommend doing so. As a PR, his chances of being approved for a US visa are greatly improved, since he'd be able to show strong ties to a comparable country, i.e. no reason at all to overstay in the US. If you apply now, the PR application won't hurt, but won't necessarily help either.
Haha fair enough, I sense the excitement building
My husband came up with similar things, didn't need any special forms. I believe the B4 pertains more to people who are moving actual stuff, like packing up your home and all your belongings, cause then you'd likely have things to declare and such. If you're entering with suitcases/luggage like any regular travel, you should be fine.