In MCE it always assumes the next paragraph to be b-quoted too, unless you specify otherwise. I think it’s default behaviour.
You could probably modify the Quote plugin so that instead of returning
<blockquote> quoted stuff </blockquote> it attached a newline character or two. Something like
<blockquote> quoted stuff </blockquote>nn might be enough as a modification, I’m not sure. MCE should interpret the two new lines as a new paragraph, hopefully without blockquotage.