Probably not. I think they just wanted the power that such an individual would bring - nothing in Dune / Dune Messiah shows them as having anything other than a relatively parochial possessiveness on the KH issue. Bear in mind that the KH they were aiming for (basically, Paul) would by no means end up with the power necessary for the GP - Leto ended up with a particular chokehold on the universe that the BG couldn't have imagined. The only reason Leto (and Paul, although he couldn't go through with it) saw the need for the GP was because of their unique capabilities as a KH - something the BG themselves didn't possess.
Conversely, the BG are later accused by Leto of recognising the need for something like the GP, but never acting to do what was needed, thus condemning him to aeons of solitude (cave writings found by Odrade).